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# Topic: Complete graph

 Complete graph - Wikipedia, the free encyclopedia In the mathematical field of graph theory a complete graph is a simple graph where an edge connects every pair of vertices. It is a regular graph of degree n − 1. They are maximally connected as the only vertex cut which disconnects the graph is the complete set of vertices. en.wikipedia.org /wiki/Complete_graph   (101 words)

 Graph theory - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-11-06) Informally, a graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs) which can be directed (assigned a direction). Another way to extend basic graphs is by making the edges to the graph directional (A links to B, but B does not necessarily link to A, as in webpages), technically called a directed graph or digraph. Graphs are represented graphically by drawing a dot for every vertex, and drawing an arc between two vertices if they are connected by an edge. en.wikipedia.org /wiki/Graph_theory   (1205 words)

 Graphs Glossary A chain in a graph is a sequence of vertices from one vertex to another using the edges. In a complete graph, all pairs of vertices are adjacent. An induced (generated) subgraph is a subset of the vertices of the graph together with all the edges of the graph between the vertices of this subset. www-math.cudenver.edu /~wcherowi/courses/m4408/glossary.htm   (1926 words)

 Graph Division A division graph is the inverse or complement of a typical graph. In general, the number of subgroups broken by a cut k is equal to the number of subgroups in the complete graph containing the cut k minus the number of m-subgraphs containing the cut k that have been broken by previous cuts. A complete m-subgraph containing a cut k is defined by the two vertices of k in addition to m-2 other vertices on the graph (chosen from n-2, as the vertices of k are already chosen). sweb.uky.edu /~jcscov0/graph_division.htm   (1308 words)

 Complete graph: Definition and Links by Encyclopedian.com - All about Complete graph   (Site not responding. Last check: 2007-11-06) A complete graph on n vertices has n vertices and n(n-1)/2 edges, and is indicated by the notation K It is a regular graph of valence n-1. A complete bipartite graph[?] is a graph with vertices segregated into two sets, where an edge connects every pair of vertices where they are not in the same set. www.encyclopedian.com /co/Complete-graph.html   (116 words)

 Maybe this Explains the Economic Cycle... best Complete Graph   (Site not responding. Last check: 2007-11-06) The Linear and Cyclic Cutwidth of the Complete Bipartite Graph The linear cutwidth of the complete bipartite graph is... Complete Graph -- from MathWorld Complete Graph -- from MathWorld A complete graph is a graph in which each pair of graph vertices is connected by an edge. ascot.pl /th/Fourier3/Complete-Graph.htm   (588 words)

 Graph Concepts   (Site not responding. Last check: 2007-11-06) A complete graph is a graph in which all vertices are adjacent to one another. A complete graph on n vertices is denoted as K(n). This is not a complete graph because not all the vertices are adjacent. www.hamline.edu /~lcopes/SciMathMN/concepts/cvocab.html   (228 words)

 graph --  Encyclopædia Britannica Graphs have the advantage of showing general tendencies in the quantitative behaviour of data, and therefore serve a predictive function. A graph G is said to be planar if it can be represented on a plane in such a fashion that the vertices are all distinct points, the edges are simple curves, and no two edges meet one another except at their terminals. The word graph may refer to the familiar curves of analytic geometry and function theory, or it may refer to simple geometric figures consisting of points and lines connecting some of these points; the latter are sometimes called linear graphs, although there is little confusion within a given context. www.britannica.com /eb/article-9037753   (671 words)

 Problems in Topological Graph Theory The genus of the complete graph minus a Hamiltonian cycle Orientable genus of graphs of bounded nonorientable genus A combinatorial generalization of drawing the complete graph www.emba.uvm.edu /~archdeac/problems/problems.html   (283 words)

 graph Formally, a graph is a set of vertices and a binary relation between vertices, adjacency. Moreover, a mathematical graph is not a comparison chart, nor a diagram with an x- and y-axis, nor a squiggly line on a stock report. GraphEd -- Graph Editor and Layout Program (C), graph manipulation (C++, C, Mathematica, and Pascal), build, traverse, top sort, etc. weighted, directed graphs (Java), JGraphT (Java) build, traverse, and display directed and undirected graphs, GEF - Graph Editing Framework (Java) a library to edit and display graphs. www.nist.gov /dads/HTML/graph.html   (539 words)

 Topological sweep of the Complete Graph   (Site not responding. Last check: 2007-11-06) We concentrate on the problem of reporting all intersections in an embedding of a complete graph that may contain degeneracies such as vertical lines, or multiply intersecting lines, where the intersections along a segment need to be reported according to the order in which they are encountered. We present a novel approach that sweeps a complete graph of N vertices and k intersection points in optimal O(k)=O(N^4) time and O(N^2) space, that is simple and easy to code and resolves the difficulties in the graph sweep. The algorithm sweeps the graph using a topological line, borrowing the concept of horizon trees from the topological sweep method [3] and using ideas from [2] to deal with degeneracies. www.cs.tufts.edu /research/geometry/graph_sweep   (365 words)

 3 Utilities Puzzle: Water, Gas, Electricity A graph is a collection of nodes (also called vertices) and edges each connecting a pair of nodes. To visualize a graph, nodes may be thought of as points in space, plane, or another surface, while edges are represented by curves connecting the nodes. A planar graph with a finite number of nodes may always be embedded into a bounded portion of the plane. www.cut-the-knot.org /do_you_know/3Utilities.shtml   (1380 words)

 COMPLETE GRAPH Complete graph A graph which has a link between every pair of nodes. A complete bipartite graph can be partitioned into two subsets of nodes such that each node is joined to every node in the other subset. An undirected graph with an edge between every pair of vertices. www.websters-online-dictionary.org /co/complete+graph.html   (270 words)

 Completely Disconnecting the Complete Graph Completely Disconnecting the Complete Graph: SIAM Journal on Discrete Mathematics Vol. In this paper we consider procedures for completely disconnecting a complete graph on \$n\$ vertices \$K_n\$. The rules are that, on each step, we may remove at most one edge from each connected component of the present graph, and in addition we may impose a limit \$w\$ on the maximum number of edges we can remove at a time. epubs.siam.org /sam-bin/dbq/article/32655   (223 words)

 Graph Theory Open Problems A graph which can be embedded in the plane so that vertices correspond to points in the plane and edges correspond to unit-length line segments is called a ``unit-distance graph.'' The question above is equivalent to asking what the chromatic number of unit-distance graphs can be. Paul O'Donnell has found a unit distance graph of girth 12 which cannot be 3-colored, but this graph has an incredibly large number of points. To get the square of an oriented graph (or any directed graph) you leave the vertex set the same, keep all the arcs, and for each pair of arcs of the form (u,v), (v,w), you add the arc (u,w) if that arc was not already present. dimacs.rutgers.edu /~hochberg/undopen/graphtheory/graphtheory.html   (705 words)

 05C: Graph theory A graph is a set V of vertices and a set E of edges -- pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on sets, which is clearly a broad topic. A graph may be viewed as a one-dimensional CW-complex and hence studied with tools from Algebraic Topology, in particular, questions of planarity (and genus). Determining the genus of a graph is NP-complete. www.math.niu.edu /~rusin/known-math/index/05CXX.html   (1204 words)

 sm342 Discrete Math, Computer lab 2   (Site not responding. Last check: 2007-11-06) The adjacency matrix for a graph is matrix whose rows and columns are indexed by the vertices (in address order) and whose i-j th entry is the number of edges from vertex i to vertex j. If one argument is used, then the complement is relative to the complete graph on the same number of vertices. For example a complete bipartite graph is specified as complete(m,n). web.usna.navy.mil /~wdj/teach/sm342/sm342_computer_lab2.html   (836 words)

 Graph Theory Glossary In a digraph (directed graph) the degree is usually divided into the in-degree and the out-degree (whose sum is the degree of the vertex in the underlying undirected graph). A digraph (or a directed graph) is a graph in which the edges are directed. A path is a sequence of consecutive edges in a graph and the length of the path is the number of edges traversed. www.utm.edu /departments/math/graph/glossary.html   (816 words)

 Graph Theory Lesson 4 A complete graph is a graph where every pair of distinct vertices are A complete graph on n vertices is denoted by K If the graph of the left is a subgraph of the graph on the right you will see its isomorphic image drawn in red in the graph on the right. www.utc.edu /Faculty/Christopher-Mawata/petersen/lesson4.htm   (392 words)

 mathematics graph   (Site not responding. Last check: 2007-11-06) Graph theory is the branch of mathematics that examines the properties of graphs. Graph -- from MathWorld Graph -- from MathWorld The word "graph" has (at least) two meanings in mathematics. In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., a plot. learning-gd.com /articles/276/mathematics-graph.html   (201 words)

 Graph Theory In an undirected graph, this is obviously a metric. A non-null graph is connected if, for every pair of vertices, there is a walk whose ends are the given vertices. A complete graph on k+1 vertices is defined to have connectivity k. www.math.fau.edu /locke/GRAPHTHE.HTM   (1173 words)

 Layered Graph Drawing A planar graph is one that can be drawn in the plane with no crossing edges. Planar graphs have been investigated for a long time, and it is known (Fáry's theorem) that any planar graph can be drawn in such a way that all edges are straight line segments. A very similar Ramsey-theoretic argument, applied to graphs formed by starting with n points and adding a new point adjacent to each triple of the n points, shows that there are also graphs with thickness three and arbitrarily large geometric thickness [Eppstein, Contemp. www.ics.uci.edu /~eppstein/junkyard/thickness   (1030 words)

 Assignment 1   (Site not responding. Last check: 2007-11-06) Every graphing calculator has a simple means to set the window to the desired dimensions. Using a piece of graph paper and a straight edge, sketch a graph of 2a above as it should appear on an exam. Using a piece of graph paper and a straight edge, sketch a graph of 2b above as it should appear on an exam. fym.la.asu.edu /%7Efym/mat210_web/lessons/Ch1/1_0/1_0_ol.htm   (1460 words)

 complete graph   (Site not responding. Last check: 2007-11-06) Definition: An undirected graph with an edge between every pair of vertices. See also sparse graph, complete tree, perfect binary tree. Paul E. Black, "complete graph", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST. www.nist.gov /dads/HTML/completeGraph.html   (87 words)

 Graph Theory Lesson 12 An Euler circuit on a graph G is a circuit that visits each vertex of G and uses every edge of G. An Euler path on a graph G is a path that visits each vertex of G and uses every edge of G. A graph that has directed edges is called a directed graph or sometimes just a digraph. www.utc.edu /~cpmawata/petersen/lesson12.htm   (469 words)

 complete graph   (Site not responding. Last check: 2007-11-06) Graphs are ways of displaying and comparing information. All graphs are neat and easy to read and, when appropriate, constructed with a straightedge. Graphs should be drawn on graph paper or resource pages. www.shs.issaquah.wednet.edu /teachers/descriptivesta/toppage19.htm   (95 words)

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