High-girth arc-transitive graphs
WebGraphs are often a natural model in real world applications such as telecommunications networks, road and transport planning, economics and social … WebIf a graph Γ is (G,s)-arc transitive and s ≤ diam(Γ), then s-geodesics and s-arcs are same, and Γ is (G,s)-geodesic transitive. However, Γ can be (G,s)-geodesic transitive but not …
High-girth arc-transitive graphs
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Webconstructed half-arc-transitive graphs of valency 2k for all integers k > 2 (see also [12]). Note that a graph of valency 2 is a disjoint union of cycles and hence not half-arc-transitive. Thus the valency of a half-arc-transitive graph is at least 4. Over the last half a century, numerous papers have been published on half-arc- Web24 de dez. de 2014 · On -arc-transitive graphs of order. We show that there exist functions and such that, if , and are positive integers with and is a -valent -arc-transitive graph of order with a prime, then . In other words, there are only finitely many -valent 2-arc-transitive graphs of order with and prime. This generalises a recent result of Conder, Li …
WebClearly λ k ≤ d k − e k, where d is the degree of Γ and e k is the maximal number of edges induced on a set of k vertices. We shall show that Cayley graphs with a prime order and … Web1 de mar. de 2001 · It is proved that if Γ is a finite connected s-transitive graph (where s ≥ 2) of order a p-power with p prime, then s = 2 or 3; further, either s = 3 and Γ is a normal …
WebAn arc in a graph is an ordered pair of adjacent vertices, and so a graph is arc-transitive if its automorphism group acts transitively on the set of arcs. As we have seen, this is a … Webinitial 3-arc will not be equivalent under any automorphism. 13(*). Let G be a distance transitive graph with girth at least five. Let k = 1. Then G is at least k-arc transitive. Consider any two k+1-arcs (they may be taken to start from the same vertex x because G is vertex-transitive). If they have an edge in common, then k-arc
Web25 de ago. de 2003 · ANALYSING FINITE LOCALLYs-ARC TRANSITIVE GRAPHS. MICHAEL GIUDICI, CAI HENG LI, AND CHERYL E. PRAEGER Abstract. We present a …
Web15 de mar. de 2011 · However, beside a well-known family of exceptional graphs, related to the lexicographic product of a cycle with an edgeless graph on two vertices, only a few such infinite families of graphs are known. In this paper, we present two more families of tetravalent arc-transitive graphs with large vertex-stabilizers, each significant for its … iphone won\u0027t turn on flashing apple logoWeb1 de mar. de 2024 · It is proved that every such graph, with the exception of the Desargues graph on 20 vertices, is either a skeleton of a hexagonal tiling of the torus, the skeleton … orange seeded eucalyptusWebTETRAVALENT ARC-TRANSITIVE GRAPHS WITH UNBOUNDED VERTEX-STABILIZERS PRIMOŽ POTOCNIK, PABLO SPIGAˇ and GABRIEL VERRET (Received … iphone won\u0027t turn on just shows apple logoWeba high level of symmetry. For example, arc-transitive 4-valent graphs of girth at most 4 were characterised in [29]. In the case of cubic graphs, even more work has been done. The structure of cubic arc-transitive graphs of girth at most 7 and 9 was studied in [12] and [7], respectively, and those of girth 6 were completely determined in [22]. iphone won\u0027t turn on only apple logoWebacts 2-arc-transitively on the quotient graph X. By Proposition 1.1, the class of finite connected 2-arc-transitive graphs can be divided into two subclasses as follows: (1) The 2-arc-transitive graphs Xwith the property that either (i) every nontrivial normal subgroup of Aut Xacts transitively on V(X),or (ii) every nontrivial normal subgroup iphone won\u0027t turn on after dyingWebLet G be a finite non-abelian simple group and let Γ be a connected tetravalent 2-arc-transitive G-regular graph. In 2004, Fang, Li, and Xu proved that either G is normal in the … iphone won\u0027t turn on flashes apple logoWebThe graph Σ is called (G, 2)-arc transitive, where G ≤ Aut(Σ), if G is transitive on the vertex set and on the set of 2-arcs of Σ. From a previous study it arises the question of when a … iphone won\u0027t turn on apple logo stuck