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Topic: Vertex-transitive

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Vertex Vertex and pixel shaders Vertex and pixel shaders are API. Vertex In polyhedron (where three or more faces and an equal number of edges meet). www.brainyencyclopedia.com /topics/vertex.html

Student/Faculty Colloquium-April 2, 2001 We will look at vertex transitive graphs, ones which have symmetries that take any vertex to any other vertex, and show that the number of ends of such a graph is 0, 1, 2 or infinity (a result of Freudenthal and Hopf). Cayley graphs of finitely generated groups (where vertices are in one-to-one correspondence with the elements of the group and edges are labelled by generators of the group, with an edge labelled g connecting vertices x and xg for all x) are good examples of vertex transitive graphs. There is a symmetry (just translate over) which takes any vertex to any other vertex, and taking large chunks out of the middle leaves two components (the ones corresponding to minus infinity and plus infinity) so that the graph has two ends. etsuodt.tamu-commerce.edu /AcademicOrganizations/sigmaxi/colloq/c040201.html

Clearing up the market cycle... best Vertex-Transitive Graph Semiregular automorphisms of vertex - transitive cubic graphs A 27- Vertex Graph That Is Vertex - Transitive and Edge- Transitive But Not 1- Transitive A 27- Vertex Graph That Is Vertex - Transitive and Edge- Transitive But Not 1- Transitive Hypertext and Postscript versions of a paper describing a 27- vertex graph... In mathematics, a vertex - transitive graph is a graph G such that, given any... ascot.pl /th/Fourier5/Vertex-Transitive-Graph.htm

Vertex code For example, a vertex at distance 7 from v is designated to be type 120 if it has 1 neighbour at distance 6 from v, 2 at distance 7 and 0 at distance 8. Now given a vertex in a cell we can classify it into one of seven types according to the cells in which its three neighbours lie. The vertex code simply counts the number of vertices of each type in each cell of the distance partition. www.csse.uwa.edu.au /~gordon/remote/foster/vertexcode.html

Transitive Transitive closure In transitive relation on X that contains R. In more concrete terms the transitive closure of R is th... Some examples of sentences with transitive verbs: I eat food. www.brainyencyclopedia.com /topics/transitive.html

Graph - graph data structures and algorithms A source vertex is defined as a vertex with successors but no predecessors: the definition means that isolated vertices are not source vertices. A sink vertex is defined as a vertex with predecessors but no successors: this definition means that isolated vertices are not sink vertices. The weaker kind is called counted, in which the edge or vertex has a count on it: add operations increase the count, and delete operations decrease the count, and once the count goes to zero, the edge or vertex is deleted. perl.enstimac.fr /perl5.8.5/site_perl/5.8.5/Graph.html

List of selected publications of Tom Snijders As an elaboration and practical implementation of this point, a statistical model for the dynamics of networks, expressed as digraphs with a fixed vertex set, is proposed in which the outdegree distribution is governed by parameters that are not connected to the parameters for the structural dynamics. For such transition matrices, a model of randomness is constructed, with a test for the hypothesis that this model holds. The elements of the dyad transition matrix, indicating the numbers of dyads of some particular type (mutual, asymmetric, of null) at time I, and of some (same or other) type at time II, are proposed as possible test statistics. stat.gamma.rug.nl /snijders/publ.htm

Edge-transitive graph - Wikipedia, the free encyclopedia In other words, a graph is edge-transitive if its automorphism group acts transitively upon its edges. In mathematics, an edge-transitive graph is a graph G such that, given any two edges e www.wikipedia.org /wiki/Edge-transitive_graph

Recent preprints by Marston Conder A tetravalent half-arc-transitive graph with nonabelian vertex stabilizer A construction is given of a 4-valent half-arc-transitive graph with vertex stabilizer isomorphic to the dihedral group D_8. The low-index subgroups procedure is an algorithm for finding all subgroups of up to a given index in a finitely-presented group $G$, and hence to determine all transitive permutation representations of $G$ of small degree. www.scitec.auckland.ac.nz /~conder/preprints

Jakob Jonsson's problem page The complex of disconnected graphs on a fixed vertex set of size n has a vertex-decomposable ( n -3)-skeleton and is homotopy equivalent to a wedge of spheres of dimension n -3. Given a family of graphs on a fixed vertex set V, we may identify the graphs in the family with their edge sets. be the matching complex on the vertex set {1, 2, 3,..., n } and let e be the 0-cell corresponding to the edge between n-1 and n. www.math.kth.se /~jakobj/myproblems.html

No Title Finite vertex transitive graphs and primitive permutation groups, in Coding Theory, Design Theory, Group Theory, (Proceedings of the Marshall Hall Conference) (Eds: D. Jungnickel and S. Vanstone), Wiley, New York, pp 51-65. Finite symmetric graphs with two-arc transitive quotients, (with Mohammad A. Iranmanesh and Sanming Zhou), J. Doubly transitive permutation groups in which the one-point stabilizer is triply transitive on a set of blocks, J. www.maths.uwa.edu.au /~praeger/CV/cherylpubs

Science Fair Projects - Cayley graph Since the action of G on itself is transitive, any Cayley graph is vertex-transitive. Explicitly, an element h sends a vertex g to the vertex h g, and the edge ( g, g s) to the edge ( h g, h g s). The Cayley graph of G with respect to S has a vertex for every element of G, with an edge from g to g s for all elements www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Cayley_graph

A 27-vertex graph that is vertex-transitive and edge-transitive but not l-transitive A graph (undirected, without loops or multiple edges) is said to be vertex-transitive if its automorphism group acts transitively on the set of vertices, edge-transitive if its automorphism group acts transitively on the set of undirected edges, and 1-transitive if its automorphism group acts transitively on the set of paths of length 1. Vertex and edge transitive, but not 1-transitive graphs. A graph which is edge transitive but not arc transitive. math.dartmouth.edu /~doyle/docs/bouwer/bouwer/bouwer.html

Uniform Polychora polyhedron or exopolyhedron to be uniform, it must be vertex transitive, and have regular polygons as faces. - this includes the polychora with wedge shaped vertex figures and their facetings (sirgax is one). - these are 4 regiments of 15, which have skewed wedge (and facetings) shaped vertex figures. members.aol.com /hedrondude/polychora.html

Vertex-transitive graph - Wikipedia, the free encyclopedia In other words, a graph is vertex-transitive if its automorphism group acts transitively upon its vertices. In mathematics, a vertex-transitive graph is a graph G such that, given any two vertices v This page was last modified 18:40, 14 May 2005. www.wikipedia.org /wiki/Vertex-transitive

Boost Graph Library: Transitive Closure The set of vertices adjacent to v in the transitive closure G* is the same as the successor set of v in the original graph G. The vertex descriptor type of the graph needs to be usable as the key type of the map. Therefore, it is redundant to compute the successor set for every vertex in a strong component; it suffices to compute it for just one vertex per component. www.boost.org /libs/graph/doc/transitive_closure.html

Graph Edge-transitive graph In automorphism f : G → G In other words, a graph is edge-transitive if its automorphism grou... Polar graph A polar graph is a graph drawn with (circular) polar coordinates. Interval graph In graph theory, an interval graph is a graph that captures the intersections among a set of intervals on... www.brainyencyclopedia.com /topics/graph.html   (756 words)

Vertex-Transitive Graphs Equivalently, each edge is subdivided with 2 new vertices, and the new vertices are joined in a cycle around the vertex at a common endpoint, which is then deleted. in which each vertex i is also joined to vertex i+k, for all i. Each vertex v of G has one or more vertices at maximum possible distance from v -- its antipodal vertices. bkocay.cs.umanitoba.ca /G&G/Transitive.html   (756 words)

Citations: Vertex transitive graphs - Sabidussi (SMEALSearch) - Pal,Rangaswamy,Giles,Debnath The set of all automorphisms forms the automorphism group Aut[ Gamma] A graph is vertex transitive if Aut[ Gamma] acts transitively on V, i.e. Then: G is transitive ( G is homogeneous G is multiplicity free ( G is commutative G is generously transitive ( G is symmetric Proof. The Hamming graphs and the Johnson graphs, for example, are distance transitive, i.e. smealsearch.psu.edu /context/11080/0   (756 words)

chapter2.html The last two results show that for a given group G there is a bijection between the equivalence classes of transitive G-actions and the conjugacy classes of subgroups in G. If one known the conjugacy classes of such subgroups, then one can describe each G-action up to equivalence. As every transitive action is equivalent to a coset action, we might ask when two coset actions are equivalent. Informally speaking, the vertices of the Cayley di-graph are the group elements, and two vertices are connected with an arc if and only if the second vertex is the product of an element from S and the first vertex. www.maths.uwa.edu.au /~csaba/4P4/chapter2.html   (756 words)

transitive_graphs Given a vertex-transitive graph G, you can attempt to describe it as a Cayley diagram. Given two vertices g and h, there certainly is an automorphism of the graph G carrying g to h, namely, the automorphism sending each vertex k to the vertex (hg^(-1))k. Let X be the automorphism group of G. If X contains no automorphisms which fix a given vertex v0, then X is in one-to-one correspondence with G (namely an automorphism x in X may be paired with the vertex x(v0); the transitivity and absence of vertex-fixers make this a one-to-one correspondence). www.math.niu.edu /~rusin/papers/known-math/96/transitive_graphs   (756 words)

Graphs, Matrices, Isomorphism For example, the cardinalities of the vertex sets must be equal, the cardinalities of the edge sets must be equal, the (ordered) degree sequences must be the same, any graph polynomials must agree on the two graphs, etc. Let M be the incidence matrix of the graph G, where the vertex labels appear in the same order as they do for A, and let D be the matrix obtained by deleting the last row of M. Therefore the automorphism group of the Peteresen graph acts transitively on paths of length three. www.math.fau.edu /locke/graphmat.htm   (756 words)

Section B is transitive on the edges of G but not on its vertices then G is bipartite. is a subgroup of Aut( G) whose action is transitive on the vertices and the edges of G. The degree of each vertex of G is even. staff.um.edu.mt /jlau/past_papers/msc97.html   (756 words)

Problem It would be interesting to find a vertex transitive graph whose matching polynomial has a nonsimple root. For every integer r there exists a vertex transitive graph G whose matching polynomial has a root of multiplicity at least r. Such a graph would not have a hamiltonian path (see [1,2]) and would disprove a conjecture of Lovasz that every vertex transitive graph has a hamiltonian path. www.fmf.uni-lj.si /~mohar/Problems/P6MatchingsVTGraphs.html   (756 words)

Problem A k-walk in G is a closed walk that visits every vertex of G and passes through any vertex at most k times. , the Petersen graph, the Coxeter graph and two graphs obtained from these by `blowing-up’ each vertex to a triangle. Let k be a positive integer and G a graph. www.fmf.uni-lj.si /~mohar/Problems/P0401VTHamiltonicity.html   (756 words)

The uniform shortest path routing conjecture For any vertex w of G the load xi(R,w) of w relative to R is the number of paths in R that contain w as an internal vertex. xi(R,w) of each vertex w in G is the same. A shortest path routing on a connected graph G of order n is a set R of n(n-1) shortest paths P_{uv} from u to v in G, where (u,v) run through all ordered pairs of distinct vertices of G. www.cs.newcastle.edu.au /Seminars/2000/Aug16.html   (756 words)

Concurrency Abstracts The basic result is that * is reflexive transitive closure, contrary to the intuition that this concept should require quantifiers for its definition. This correspondence shows this generalization of categories to be a close cousin to the generalization of transitive closure algorithms. The motivating application is a uniform theory of abstract or parametrized time in which to any given notion of time there corresponds an algebra of concurrent behaviors and their operations, always the same operations but interpreted automatically and appropriately for that notion of time. boole.stanford.edu /abstracts.html   (756 words)

Abstracts of papers by Peter J. Cameron In the finite case, all graphs on a given set of vertices are equivalent under switching, and we determine the structure of the switching group and show that its extension by the symmetric group on the vertex set is primitive. A relational structure A satisfies the P( n,k) property if whenever the vertex set of A is partitioned into n nonempty parts, the substructure induced by the union of some k of the parts is isomorphic to A. The main new result of the paper is an elementary proof of part of a theorem of Macpherson and Praeger, according to which a group which preserves no non-trivial topology is highly transitive. www.maths.qmul.ac.uk /~pjc/abstracts.html   (756 words)

Goldstone Abstract In this talk we consider conditions under which a vertex transitive graph becomes disconnected when a vertex and all its immediate neighbors are removed. This condition is sufficient for a certain class of vertex transitive graphs to which all cases can be reduced. More specifically, we discuss a necessary condition phrased in terms of neighborhoods of the deleted vertex and the stabilizer of a particular subset of the neighborhoods. math.smith.edu /~rhaas/cone/abs/goldstone.html   (756 words)

93-05-031 The relationship of orthogonal functions associated with vertex transitive graphs and random walks on such graphs is investigated. We use this relations to characterize the exponentially decaying autocorrelation functions along random walks on isotropic random fields defined on vertex transitive graphs. The results are applied to a simple spin glass model. www.tbi.univie.ac.at /papers/Abstracts/93-05-031abs.html   (756 words)

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