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Real-world problems in inequalities are solved using the TI-Nspire graphing calculator. These include inequalities with one or two variables and situations such as predicting the break-even point of a start-up business. Basic vocabulary for dealing with inequalities is introduced and illustrated. Two problems are illustrated without comment while others are developed step-by-step from the definit...
Introduces the use of the Texas Instruments' TI-Nspire graphic calculator to solve real-life problems involving functions and relations. Examples range from the lift-off and pre-orbital path of a rocket, to a rocket in orbit, to the orbits of planets, to the trajectory of a spacecraft traveling to Mars. The graphic calculator is used to calculate parabolic, circular and elliptical paths.This produ...
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High Quality Content by WIKIPEDIA articles In the mathematical field of graph theory, a complete graph is a simple graph in which every pair of distinct vertices is connected by an edge. The complete graph on n vertices has n vertices and n(n1)/2 edges, and is denoted by (from the German komplett). It is a regular graph of degree . All complete graphs are their own cliques. They are maximally connected as the only vertex cut which disconnects the graph is the complete set of vertices. Author: Miller, Frederic P./ Vandome, Agnes F./ McBrewster, John Binding Type: Paperback Number of Pages: 128 Publication Date: 2010/07/30 Language: English Dimensions: 5.98 x 9.01 x 0.30 inches
High Quality Content by WIKIPEDIA articles In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. Formally, a signed graph is a pair (G, ) that consists of a graph G = (V, E) and a sign mapping or signature from E to the sign group {+, }. The graph may have loops and multiple edges as well as halfedges (with only one endpoint) and loose edges (with no endpoints). Half and loose edges do not receive signs. (In the terminology of the article on graphs, it is a multigraph, but we say graph because in signed graph theory it is usually unnatural to restrict to simple graphs.) The sign of a circle (this is the edge set of a simple cycle) is defined to be the product of the signs of its edges; in other words, a circle is positive if it contains an even number of negative edges and negative if it contains an odd number of negative edges. The fundamental fact about a signed graph is the list of positive circles, which we write B( ). Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 90 Publication Date: 2010/08/12 Language: English Dimensions: 6.00 x 9.02 x 0.22 inches
In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. For example, a graph may be constructed by choosing the vertices to be the first 1000 positive integers, and defining that there is an edge between two vertices if and only if those two integers have at least one decimal digit in common. In other cases the relationship between vertices is not symmetric: for example, a graph may be constructed by choosing the vertices to be the first 1000 positive integers, and defining that there is an edge from i to j if i is a divisor of j. This type of graph is called a directed graph and the edges are called directed edges or arcs; in contrast, a graph where the edges are not directed is called undirected. Vertices are also called nodes or points, and edges are also called lines. Graphs are the basic subject studied by graph theory. Author: Miller, Frederic P./ Vandome, Agnes F./ McBrewster, John Binding Type: Paperback Number of Pages: 96 Publication Date: 2009/11/23 Language: English Dimensions: 5.98 x 9.01 x 0.22 inches
High Quality Content by WIKIPEDIA articles In computational geometry and robot motion planning, a visibility graph is a graph of intervisible locations, typically for a set of points and obstacles in the Euclidean plane. Each node in the graph represents a point location, and each edge represents a visible connection between them. That is, if the line segment connecting two locations does not pass through any obstacle, an edge is drawn between them in the graph. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 126 Publication Date: 2010/08/04 Language: English Dimensions: 6.00 x 9.02 x 0.30 inches
High Quality Content by WIKIPEDIA articles In graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split graphs were first studied by Foldes and Hammer (1977a, 1977b), and independently introduced by Tyshkevich and Chernyak (1979). Note that the partition into a clique and an independent set need not be unique; for instance, the path abc is a split graph, the vertices of which can be partitioned in three different ways: 1. the clique {a, b} and the independent set {c} 2. the clique {b, c} and the independent set {a} 3. the clique {b} and the independent set {a, c} Split graphs can be characterized in terms of their forbidden induced subgraphs: a graph is split if and only if no induced subgraph is a cycle on four or five vertices, or a pair of disjoint edges (the complement of a 4cycle). Author: Surhone, Lambert M./ Tennoe, Mariam T./ Henssonow, Susan F. Binding Type: Paperback Number of Pages: 90 Publication Date: 2010/08/13 Language: English Dimensions: 6.00 x 9.02 x 0.22 inches
High Quality Content by WIKIPEDIA articles In graph theory, a graph G with vertex set V(G) is said to be kvertexconnected (or kconnected) for k Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 64 Publication Date: 2010/08/09 Language: English Dimensions: 5.98 x 9.00 x 0.15 inches
PMHigh Quality Content by WIKIPEDIA articles The Turan graph T(n,r) is a graph formed by partitioning a set of n vertices into r subsets, with sizes as equal as possible, and connecting two vertices by an edge whenever they belong to different subsets. The graph will have (nmod r) subsets of size lceil n/rrceil, and r (nmod r) subsets of size lfloor n/rrfloor. That is, it is a complete rpartite graph K_{lceil n/rrceil, lceil n/rrceil, ldots, lfloor n/rrfloor, lfloor n/rrfloor}. Each vertex has degree either nlceil n/rrceil or nlfloor n/rrfloor. The number of edges is at most left(1frac1rright)frac{n 2}{2}. It is a regular graph, if n is divisible by Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 90 Publication Date: 2010/08/09 Language: English Dimensions: 6.00 x 9.02 x 0.22 inches
High Quality Content by WIKIPEDIA articles In software testing, a causeeffect graph is a directed graph that maps a set of causes to a set of effects. The causes may be thought of as the input to the program, and the effects may be thought of as the output. Usually the graph shows the nodes representing the causes on the left side and the nodes representing the effects on the right side. There may be intermediate nodes in between that combine inputs using logical operators such as AND and OR. Constraints may be added to the causes and effects. These are represented as edges labelled with the constraint symbol using a dashed line. For causes, valid constraint symbols are E (exclusive), O (one and only one), and I (at least one). The exclusive constraint states that both causes1 and cause2 cannot be true simultaneously. The Inclusive (at least one) cons Author: Surhone, Lambert M./ Tennoe, Mariam T./ Henssonow, Susan F. Binding Type: Paperback Number of Pages: 112 Publication Date: 2010/09/20 Language: English Dimensions: 6.00 x 9.02 x 0.27 inches
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Graph transformation, or Graph rewriting, concerns the technique of creating a new graph out of an original graph using some automatic machine. It has numerous applications, ranging from software verification to layout algorithms. Graph transformations can be used as a computation abstraction. The basic idea is that the state of a computation can be represented as a graph, further steps in that computation can then be represented as transformation rules on that graph. Such rules consist of an original graph, which is to be matched to a subgraph in the complete state, and a replacing graph, which will replace the matched subgraph. Formally, a graph rewriting system consists of a set of graph rewrite rules of the form, with L being called pattern graph and R being called replacement graph. A graph rewrite rule is applied to the host graph by searching for an occurrence of the pattern graph and by replacing the found occurrence by an instance of the replacement graph. Author: Trev, Nuadha Binding Type: Paperback Number of Pages: 84 Publication Date: 2011/08/16 Language: English Dimensions: 9.02 x 5.98 x 0.20 inches
High Quality Content by WIKIPEDIA articles In graph theory, a vertex (plural vertices) or node is the fundamental unit out of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices). From the point of view of graph theory, vertices are treated as featureless and indivisible objects, although they may have additional structure depending on the application from which the graph arises; for instance, a semantic network is a graph in which the vertices represent concepts or classes of objects. The two vertices forming an edge are said to be its endpoints, and the edge is said to be incident to the vertices. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 78 Publication Date: 2010/08/09 Language: English Dimensions: 6.00 x 9.02 x 0.19 inches
High Quality Content by WIKIPEDIA articles High Quality Content by WIKIPEDIA articles In the area of mathematics called combinatorial group theory, the Schreier coset graph is a graph associated to a group G, a generating set { xi: i in I }, and a subgroup H G. The vertices of the graph are the right cosets Hg = { hg: h in G } for g in G. The edges of the graph are of the form (Hg, Hgxi). The Cayley graph of the group G with { xi: i in I } is the Schreier coset graph for H = { 1G }. The graph is named after Otto Schreier. The graph is useful to understand coset enumeration and the ToddCoxeter algorithm. A spanning tree of a Schreier coset graph corresponds to a Schreier transversal, as in Schreiers subgroup lemma, (Conder 2003). Coset graphs can be used to form large permutation representations of groups and were used by Graham Higman to show that the alternating groups of large enough degree are Hurwitz groups, (Conder 2003). Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 90 Publication Date: 2010/08/10 Language: English Dimensions: 6.00 x 9.02 x 0.22 inches
High Quality Content by WIKIPEDIA articles In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices. It may also be an entire graph consisting of edges without common vertices. Author: Miller, Frederic P./ Vandome, Agnes F./ McBrewster, John Binding Type: Paperback Number of Pages: 92 Publication Date: 2010/09/29 Language: English Dimensions: 6.00 x 9.02 x 0.22 inches
We present a generalized (multitype) version of percolation on the complete graph, in which we divide the vertices of the graph into a fixed number of sets (called layers) and perform percolation where the probability of {u, v} being in our edge set depends on the respective layers of u and v. Many results analogous to usual percolation on the complete graph are determined. In addition, we determine the exponential rate function for the probability that a giant component occupies a fixed fraction of the graph, while all other components are small. We also determine the exponential rate function for the probability that a particular exploration process on the random graph will discover a certain fraction of vertices in each layer, without encountering a giant component. Author: Smith, S. Alex Binding Type: Paperback Number of Pages: 58 Publication Date: 2011/09/03 Language: English Dimensions: 9.69 x 7.44 x 0.12 inches
High Quality Content by WIKIPEDIA articles Planar straightline graph (PSLG) is a term used in computational geometry for an embedding of a planar graph in the plane such that its edges are mapped into straight line segments. Farys theorem (1948) states that every planar graph has this kind of embedding. In computational geometry PSLGs have often been called planar subdivisions, with an assumption or assertion that subdivisions are polygonal. A PSLG without vertices of degree 1 defines a subdivision of the plane into polygonal regions and vice versa. The absence of vertices of degree 1 simplifies descriptions of various algorithms, but it is not essential. PSLGs may serve as representations of various maps, e.g., geographical maps in geographical information systems. Special cases of PSLGs are triangulations (polygon triangulation, point set triangulation). Point set triangulations are maximal PSLGs in the sense that it is impossible to add straight edges to them. Triangulations have numerous applications in various areas. Author: Surhone, Lambert M./ Tennoe, Mariam T./ Henssonow, Susan F. Binding Type: Paperback Number of Pages: 106 Publication Date: 2010/08/16 Language: English Dimensions: 5.98 x 9.00 x 0.25 inches
This book presents two major research results on the fast implementation of graph rewriting systems (GRS). First, it explores the class of socalled UBSGRS, where the complexity of a rewriting step is linear instead of NP, showing for example that visual programming is possible by UBS graph rewriting. Second, an abstract machine for graph rewriting is defined providing an instruction set sufficient for the execution of GRS.The basic definitions of GRS in the algorithmic approach are introduced and extended by attribution and control structures to comprise a formalism for an operational specification. The translation of a functional programming language to graph rewriting shows the capabilities of UBSGRS. Author: Dorr, Heiko/ Dvrr, Heiko/ Darr, Heiko Series Title: Lecture Notes in Computer Science Series Number: 922 Binding Type: Paperback Number of Pages: 275 Publication Date: 1995/08/25 Language: English Dimensions: 9.21 x 6.14 x 0.60 inches
High Quality Content by WIKIPEDIA articles An Erd sDiophantine graph is an object in the mathematical subject of Diophantine geometry consisting of a set of integer points at integer distances in the plane that cannot be extended by any additional points. Equivalently, it can be described as a complete graph with vertices located on the integer square grid Z such that all mutual distances between the vertices are integers, while all other grid points have a noninteger distance to at least one vertex. Erd sDiophantine graphs are named after Paul Erd s and Diophantus of Alexandria. They form a subset of the set of Diophantine figures, which are defined as complete graphs in the Diophantine plane for which the length of all edges are integers. Thus, Erd sDiophantine graphs are exactly the Diophantine figures that cannot be extended. The existence of Erd sDiophantine graphs follows from the Erd sAnning theorem, Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 100 Publication Date: 2010/08/12 Language: English Dimensions: 5.98 x 9.00 x 0.24 inches
A Deltasystem is a hypergraph with hyperedges A 1, ..., Ak such that there is a set K such that if i j, then Ai cap; Aj = K. The classical Sunflower Lemma of Erdos and Rado asserts that any runiform set system with at least (r 1) kr edges contains a Deltasystem with k hyperedges. In this dissertation, we demonstrate methods based on the Sunflower Lemma used to solve a variety of problems in graph theory. The first of these problems is one in the field of graph minors. We prove a conjecture of Myers that, for every fixed positive integer s and every integer t sufficiently large with respect to s, there is a constant C such that every graph with average degree at least C t contains a minor isomorphic to Ks, t. In fact, we determine asymptotically (in s) the smallest average degree that forces a graph to contain a Ks, tminor, and in the case s = 3, we determine the smallest such average degree exactly. The second problem we study is one in the field of domination in graphs. We develop methods for proving NordhausGaddum bounds on the kdomination number of a graph for any positive integer k. We prove such bounds when k = 1 and apply the method used to derive similar bounds on parameters of the same order of magnitude as the domination number. We then extend the bounds to arbitrary k > 1. We close our study of domination by considering when the ratio of the Roman domination number of a graph to its domination number is either 1 or 2. Our final problem is one in graph representations. We develop a lemma on traces of hypergraphs, extending results of Balogh and Bollobas. We then use this lemma, along with probabilistic methods, to show that for every positive integer k, almost every graph has no kminimumdifferencerepresentation. This answers a question of Boros, Gurvich, and Meshulam. Author: Prince, Noah B. Binding Type: Paperback Number of Pages: 112 Publication Date: 2011/09/02 Language: English Dimensions: 9.69 x 7.44 x 0.23 inches
This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering including: mobile sensor networks distributed robotics such as formation flying and swarming quantum networks networked economics biological synchronization and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks the book presents a powerful new formalism and set of tools for networked systems. The book's three sections look at foundations multiagent networks and networks as systems. The authors give an overview of important ideas from graph theory followed by a detailed account of the agreement protocol and its various extensions including the behavior of the protocol over undirected directed switching and random networks. They cover topics such as formation control coverage distributed estimation social networks and games over networks. And they explore intriguing aspects of viewing networks as systems by making these networks amenable to control-theoretic analysis and automatic synthesis by monitoring their dynamic evolution and by examining higher-order interaction models in terms of simplicial complexes and their applications. The book will interest graduate students working in systems and control as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications.
High Quality Content by WIKIPEDIA articles In the mathematical field of graph theory, the Shrikhande graph is a named graph discovered by S. S. Shrikhande in 1959. It is a strongly regular graph with 16 vertices and 48 edges, with each vertex having a degree of 6. In the Shrikhande graph, any two vertices I and J have two distinct neighbors in common (excluding the two vertices I and J themselves), which holds true whether or not I is adjacent to J. In other words, its parameters for being strongly regular are: {16,6,2,2}, with = = 2, this equality implying that the graph is associated with a symmetric BIBD. It shares these parameters with a different graph, the 4x4 rooks graph. The Shrikhande graph is locally hexagonal; that is, the neighbors of each vertex form a cycle of six vertices. As with any locally cyclic graph, the Shrikhande graph is the 1skeleton of a Whitney triangulation of some surface; in the case of the Shrikhande graph, this surface is a torus in which each vertex is surrounded by six triangles. Thus, the Shrikhande graph is a toroidal graph. The dual of this embedding is the Dyck graph, a cubic symmetric graph. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 102 Publication Date: 2010/08/11 Language: English Dimensions: 6.00 x 9.02 x 0.24 inches
High Quality Content by WIKIPEDIA articles An ordered graph is a graph with a total order over its nodes.The induced graph of an ordered graph is obtained by adding some edges to an ordering graph, using the method outlined below. The induced width of an ordered graph is the width of its induced graph. Given an ordered graph, its induced graph is another ordered graph obtained by joining some pairs of nodes that are both parents of another node. In particular, nodes are considered in turn according to the ordering, from last to first. For each node, if two of its parents are not joined by an edge, that edge is added. In other words, when considering node n, if both m and l are parents of it and are not joined by an edge, the edge (m, l) is added to the graph. Since the parents of a node are always connected with each other, the induced graph is always chordal. As an example, the induced graph of an ordered graph is calculated Author: Surhone, Lambert M./ Tennoe, Mariam T./ Henssonow, Susan F. Binding Type: Paperback Number of Pages: 66 Publication Date: 2010/08/17 Language: English Dimensions: 6.00 x 9.02 x 0.16 inches
High Quality Content by WIKIPEDIA articles In the mathematical field of graph theory, the Robertson graph or (4,5)cage is a 4regular undirected graph with 19 vertices and 38 edges named after Neil Robertson. The Robertson graph is the unique (4,5)cage graph and was discovered by Robertson in 1964. As a cage graph, it is the smallest 4regular graph with girth 5. It has chromatic number 3, chromatic index 5, diameter 3, radius 3 and is both 4vertexconnected and 4edgeconnected. The Robertson graph is also a Hamiltonian graph which possesses 5,376 distinct directed Hamiltonian cycles. Author: Surhone, Lambert M./ Tennoe, Mariam T./ Henssonow, Susan F. Binding Type: Paperback Number of Pages: 90 Publication Date: 2010/08/15 Language: English Dimensions: 6.00 x 9.02 x 0.22 inches
High Quality Content by WIKIPEDIA articles In mathematics, a graph G is toroidal if it can be embedded on the torus. In other words, the graphs vertices can be placed on a torus such that no edges cross. Usually, it is assumed that G is also nonplanar.The Heawood graph, the complete graph K7 (and hence K5 and K6), the Petersen graph (and hence the complete bipartite graph K3,3, since the Petersen graph contains a subdivision of it), the Blanu a snarks, (Orbani et al. 2004) and all Mobius ladders are toroidal. More generally, any graph with crossing number 1 is toroidal. Some graphs with greater crossing numbers are also toroidal: the MobiusKantor graph, for example, has crossing number 4 and is toroidal (Maru i Pisanski 2000). Author: Surhone, Lambert M./ Tennoe, Mariam T./ Henssonow, Susan F. Binding Type: Paperback Number of Pages: 90 Publication Date: 2010/08/14 Language: English Dimensions: 6.00 x 9.02 x 0.22 inches
High Quality Content by WIKIPEDIA articles Graph drawing or Graph layout, as a branch of graph theory, applies topology and geometry to derive twodimensional representations of graphs. A drawing of a graph is basically a pictorial representation of an embedding of the graph in the plane, usually aimed at a convenient visualization of certain properties of the graph in question or of the object modeled by the graph. Graph drawing is motivated by applications such as VLSI circuit design, social network analysis, cartography, and bioinformatics, many of which make use of information visualization. Author: Surhone, Lambert M./ Tennoe, Mariam T./ Henssonow, Susan F. Binding Type: Paperback Number of Pages: 136 Publication Date: 2010/08/15 Language: English Dimensions: 6.00 x 9.02 x 0.32 inches
High Quality Content by WIKIPEDIA articles The terms lattice graph, mesh graph, or grid graph refer to a number of categories of graphs whose drawing corresponds to some grid/mesh/lattice, i.e., its vertices correspond to the nodes of the mesh and its edges correspond to the ties between the nodes. A common type of a lattice graph (known under different names, such as square grid graph) is the graph whose vertices correspond to the points in the plane with integer coordinates, xcoordinates being in the range 0, ..., n, ycoordinates being in the range 1, ...m, and two vertices are connected by an edge whenever the corresponding points are at distance 1. In other words, it is a unit distance graph for the described point se Author: Miller, Frederic P./ Vandome, Agnes F./ McBrewster, John Binding Type: Paperback Number of Pages: 80 Publication Date: 2010/08/21 Language: English Dimensions: 6.00 x 9.02 x 0.19 inches
In graph theory, an area of mathematics, a clawfree graph is a graph that does not have a claw as an induced subgraph. A claw is another name for the complete bipartite graph K1,3 (that is, a star graph with three edges, three leaves, and one central vertex). A clawfree graph is a graph in which no induced subgraph is a claw; i.e., any subset of four vertices has other than only three edges connecting them in this pattern. Equivalently, a clawfree graph is a graph in which the neighborhood of any vertex is the complement of a trianglefree graph. Clawfree graphs were initially studied as a generalization of line graphs, and gained additional motivation through three key discoveries about them: the fact that all such graphs have perfect matchings, the discovery of polynomial time algorithms for finding maximum independent sets in claw free graphs, and the characterization of clawfree perfect graphs. They are the subject of hundreds of mathematical research papers and several surveys. Author: Miller, Frederic P./ Vandome, Agnes F./ McBrewster, John Binding Type: Paperback Number of Pages: 74 Publication Date: 2010/04/24 Language: English Dimensions: 5.98 x 9.01 x 0.17 inches
High Quality Content by WIKIPEDIA articles In the mathematical discipline of graph theory, a wheel graph Wn is a graph with n vertices, formed by connecting a single vertex to all vertices of an (n1)cycle. The numerical notation for wheels is used inconsistently in the literature: some authors instead use n to refer to the length of the cycle, so that their Wn is the graph we denote Wn+1. A wheel graph can also be defined as the 1skeleton of an (n1)gonal pyramid. Wheel graphs are planar graphs, and as such have a unique planar embedding. More specifically, every wheel graph is a Halin graph. They are selfdual: the planar dual of any wheel graph is an isomorphic graph. Any maximal planar graph, other than K4 = W4, contains as a subgraph either W5 or W6. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 70 Publication Date: 2010/08/12 Language: English Dimensions: 6.00 x 9.02 x 0.17 inches
High Quality Content by WIKIPEDIA articles Rooks graphs are vertextransitive and (n + m 2)regular; they are the only regular graphs formed from the moves of standard chess pieces in this way (Elkies). When m n, the symmetries of the rooks graph are formed by independently permuting the rows and columns of the graph. When n = m the graph has additional symmetries that swap the rows and columns; the rooks graph for a square chessboard is symmetric. Any two vertices in a rooks graph are either at distance one or two from each other, according to whether they are adjacent or nonadjacent respectively. Any two nonadjacent vertices may be transformed into any other two nonadjacent vertices by a symmetry of the graph. When the rooks graph is not square, the pairs of adjacent vertices fall into two orbits of the symmetry group according to whether they are adjacent horizontally or vertically, but when the graph is square any two adjacent vertices may also be mapped into each other by a symmetry and the graph is therefore distancetransitive. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 70 Publication Date: 2010/08/11 Language: English Dimensions: 6.00 x 9.02 x 0.17 inches
High Quality Content by WIKIPEDIA articles In mathematics, the Coates graph or Coates flow graph, named after C.L. Coates, is a graph associated with the Coates method for the solution of a system of linear equations. The Coates graph Gc(A) associated with an n x n matrix A is an nnode, weighted, labeled, directed graph. The nodes, labeled 1 through n, are each associated with the corresponding row/column of A. If entry aji 0 then there is a directed edge from node i to node j with weight aji. In other words, the Coates graph for matrix A is the one whose adjacency matrix is the transpose of A. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 122 Publication Date: 2010/08/09 Language: English Dimensions: 6.00 x 9.02 x 0.29 inches
This thoroughly revised second edition of Shimon Even's Graph Algorithms explains algorithms directly and intuitively, in formal but simple language.
High Quality Content by WIKIPEDIA articles A threedimensional graph is the graph of a function of two variables f(x, y). Provided that x, y, and f(x, y) are real numbers, the graph can be represented as a planar or curved surface in a threedimensional Cartesian coordinate system. In mathematics, the graph of a function f is the collection of all ordered pairs (x, f(x)). In particular, if x is a real number, graph means the graphical representation of this collection, in the form of a curve on a Cartesian plane, together with Cartesian axes, etc. Graphing on a Cartesian plane is sometimes referred to as curve sketching. If the function input x is an ordered pair (x1, x2) of real numbers, the graph is the collection of all ordered triples (x1, x2, f(x1, x2)), and its graphical representation is a surface (see three dimensional graph). Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 100 Publication Date: 2010/08/09 Language: English Dimensions: 5.98 x 9.00 x 0.24 inches
Explores connections between major topics in graph theory and graph colorings. This book presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings.
High Quality Content by WIKIPEDIA articles In the mathematical field of graph theory, a distancetransitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y. A distance transitive graph is vertex transitive and symmetric as well as distance regular. A distancetransitive graph is interesting partly because it has a large automorphism group. Some interesting finite groups are the automorphism groups of distancetransitive graphs, especially of those whose diameter is 2. Distancetransitive graphs were first defined in 1971 by Norman L. Biggs and D. H. Smith, who showed that there are only 12 finite trivalent distancetransitive graphs. Author: Toll Aaron Philippe, Aaron Philippe/ Miller, Frederic P./ Vandome, Agnes F. Binding Type: Paperback Number of Pages: 76 Publication Date: 2010/06/25 Language: English Dimensions: 5.98 x 9.01 x 0.18 inches
High Quality Content by WIKIPEDIA articles An entitative graph is an element of the graphical syntax for logic that Charles Sanders Peirce developed under the name of qualitative logic beginning in the 1880s, taking the coverage of the formalism only as far as the propositional or sentential aspects of logic are concerned. See 3.468, 4.434, and 4.564 in Peirces Collected Papers.A proof manipulates a graph, using a short list of rules, until the graph is reduced to an empty cut or the blank page. A graph that can be so reduced is what is now called a tautology (or the complement thereof). Graphs that cannot be simplified beyond a certain point are analogues of the satisfiable formulas of firstorder logic. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 106 Publication Date: 2010/08/11 Language: English Dimensions: 6.00 x 9.02 x 0.25 inches
High Quality Content by WIKIPEDIA articles A scene graph is a general data structure commonly used by vectorbased graphics editing applications and modern computer games. Examples of such programs include AutoCAD, Adobe Illustrator, Acrobat 3D, X3D, VRML97, OpenSceneGraph, OpenSG, and CorelDRAW. The scene graph is a structure that arranges the logical and often (but not necessarily) spatial representation of a graphical scene. The definition of a scene graph is fuzzy because programmers who implement scene graphs in applications and in particular the games industry take the basic principles and adapt these to suit particular applications. This means there is no consensus as to what a scene graph should be. Author: Surhone, Lambert M./ Tennoe, Mariam T./ Henssonow, Susan F. Binding Type: Paperback Number of Pages: 92 Publication Date: 2010/09/27 Language: English Dimensions: 6.00 x 9.02 x 0.22 inches
High Quality Content by WIKIPEDIA articles In the mathematical study of graph theory, a pancyclic graph is a directed or undirected graph that contains cycles of all possible lengths from three up to the number of vertices in the graph. Pancyclic graphs are a generalization of Hamiltonian graphs, graphs which have a cycle of the maximum possible length. A tournament is a directed graph with one directed edge between each pair of vertices. Intuitively, a tournament can be used to model a roundrobin sports competition, by drawing an edge from the winner to the loser of each game in the competition. A tournament is called strongly connected or strong if and only if it cannot be partitioned into two subsets L and W of losers and winners, such that every competitor in W beats every competitor in L. Every strong tournament is pancyclic and nodepancyclic. Author: Miller, Frederic P./ Vandome, Agnes F./ McBrewster, John Binding Type: Paperback Number of Pages: 76 Publication Date: 2010/10/09 Language: English Dimensions: 6.00 x 9.02 x 0.18 inches
High Quality Content by WIKIPEDIA articles A twodimensional graph is the graph of a function of one variable f(x). Provided that x and f(x) are real numbers, the graph can be represented as a straight or curved curve in a twodimensional Cartesian coordinate system.A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin. The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as a signed distances from the origin. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 104 Publication Date: 2010/08/09 Language: English Dimensions: 5.98 x 9.00 x 0.25 inches
High Quality Content by WIKIPEDIA articles In mathematics, a dual graph of a given planar graph G is a graph which has a vertex for each plane region of G, and an edge for each edge in G joining two neighboring regions, for a certain embedding of G. The term dual is used because this property is symmetric, meaning that if H is a dual of G, then G is a dual of H (if G is connected). The same notation of duality may also be used for more general embeddings of graphs on manifolds. Author: Surhone, Lambert M./ Tennoe, Mariam T./ Henssonow, Susan F. Binding Type: Paperback Number of Pages: 112 Publication Date: 2010/08/15 Language: English Dimensions: 6.00 x 9.02 x 0.27 inches
High Quality Content by WIKIPEDIA articles Microsoft Graph (also known as Microsoft Chart) is an OLE application that is deployed by a number of the Microsoft Office programs such as Excel and Access to create charts and graphs. The program can also be hosted as an OLE application object in Visual Basic. Microsoft Graph supports many different types of charts, however, it is a legacy application and the charts produced are not modernlooking and polished. Office 2003 was the last version to use Microsoft Graph for hosting charts inside Office applications as OLE objects. Office 2007, specifically, Excel 2007 includes a new integrated highquality charting engine and the charts created are native to the applications. The new engine supports advanced formatting, including 3D rendering, transparencies and shadows. Chart layouts can also be customized to highlight various trends in the data. Microsoft Graph still exists for compatibility reasons, but the entry points are removed. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 184 Publication Date: 2010/08/11 Language: English Dimensions: 6.00 x 9.02 x 0.42 inches
High Quality Content by WIKIPEDIA articles A Tanner graph is a bipartite graph used to specify constraints or equations which specify error correcting codes. In coding theory, Tanner graphs are used to construct longer codes from smaller ones. Both encoders and decoders employ these graphs extensively. Tanner graphs were proposed by Michael Tanner as a means to create larger error correcting codes from smaller ones using recursive techniques. He generalized the techniques of Elias for product codes. Tanner discussed lower bounds on the codes obtained from these graphs irrespective of the specific characteristics of the codes which were being used to construct larger codes. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 82 Publication Date: 2010/08/10 Language: English Dimensions: 6.00 x 9.02 x 0.20 inches
Deals with graph data analytics. This book contains surveys on the graph topics like graph languages, indexing, clustering, data generation, pattern mining, classification, keyword search, pattern matching, and privacy. It also studies various domain-specific scenarios like stream mining, web graphs, social networks, chemical and biological data.
High Quality Content by WIKIPEDIA articles A selfcomplementary graph is a graph which is isomorphic to its complement. The simplest selfcomplementary graphs are the 4vertex path graph and the 5vertex cycle graph.Selfcomplementary graphs are interesting in their relation to the graph isomorphism problem: the problems of checking whether two selfcomplementary graphs are isomorphic and of checking whether a given graph is selfcomplementary are polynomialtime equivalent to the general graph isomorphism problem. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 64 Publication Date: 2010/08/10 Language: English Dimensions: 5.98 x 9.00 x 0.15 inches
High Quality Content by WIKIPEDIA articles A trellis is a graph of which the nodes are ordered into vertical slices (time) and each node at each time is connected to (at least) one node at an earlier and (at least) one node at a later time. The earliest and latest times in the trellis have only one node.Trellises are used in encoders and decoders for communication theory and encryption. They are also the central datatype used in BaumWelch algorithm for Hidden Markov Models. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 70 Publication Date: 2010/08/10 Language: English Dimensions: 6.00 x 9.02 x 0.17 inches
For the Brother GT-541 Garment Printer, set the Timer for 35 Seconds. MS158 Automatically Lifts the Heat Plate Up for fabric removal so you don't burn standard cotton tshirts.Insta Graph MS-158 Digi Press USA, Auto Release Heat Set Clam Press, InstaGraph MS158, 15x20" for Brother GT541 Ink Jet DTG Direct to Garment Printer
For the Brother GT-541 Garment Printer, set the Timer for 35 Seconds. MS138 Automatically Lifts the Heat Plate Up for fabric removal so you don't burn standard cotton tshirts.Insta Graph MS-138 Digi Press USA, Heat Set Clam Press, InstaGraph MS138, 15x20", Brother GT-541 Ink Jet DTG Direct to Garment Printer
Provides the source code for a library of Java programs that can be used to solve problems in graph theory and combinatorial optimization. This book covers random graph generation and connectivity procedures. It deals with topics such as graph coloring, graph matching, network flow, and packing and covering, including the assignment, and others.
High Quality Content by WIKIPEDIA articles A logical graph is a special type of diagramatic structure in any one of several systems of graphical syntax that Charles Sanders Peirce developed for logic. In his papers on qualitative logic, entitative graphs, and existential graphs, Peirce developed several versions of a graphical formalism, or a graphtheoretic formal language, designed to be interpreted for logic. In the century since Peirce initiated this line of development, a variety of formal systems have branched out from what is abstractly the same formal base of graphtheoretic structures. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 154 Publication Date: 2010/08/11 Language: English Dimensions: 6.00 x 9.02 x 0.36 inches
US $9.19
