High-girth arc-transitive graphs
Weba 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]. WebThe Cayley graph F is denoted by Cay(G, S). Cayley graphs stem from a type of diagram now called a Cayley color diagram, introduced by Cayley in 1878. In this paper, we …
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- 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 …
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 … Web4 de mai. de 2024 · In this paper, a complete classification of finite simple cubic vertex-transitive graphs of girth $6$ is obtained. It is proved that every such graph, with the exception of the Desargues graph on ...
Web1 de ago. de 2010 · A near-polygonal graph is a graph Γ which has a set C of m-cycles for some positive integer m such that each 2-path of Γ is contained in exactly one cycle in C.If m is the girth of Γ then the graph is called polygonal. We provide a construction of an infinite family of polygonal graphs of arbitrary odd girth with 2-arc transitive automorphism … 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 …
WebThe study of cubic s-arc-transitive graphs goes back to the seminal papers of Tutte [14, 15] who showed that s ≤ 5. More generally, Weiss [16] proved that s ≤ 7for graphs of …
WebA. A. Ivanov [4] found a relationship between 2-arc-transitive graphs of girth 5 and flag-transitive geometries with the diagram P L O 0 0 In particular, such a geometry can … iron tablet that doesn\u0027t cause constipationWebLet 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 … iron table and chairs for patioWebIf 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 … iron tablets 27WebGraphs are often a natural model in real world applications such as telecommunications networks, road and transport planning, economics and social … port st lucie fl death noticesWebtransitive graphs that are s-arc transitive but not (s+1)-arc transitive. More-over, there exist geodesic transitive graphs that are s-arc transitive but not (s+1)-arc transitive with arbitrarily large diameter if and only if s ∈ {1,2,3}. Theorem 1.1 is proved in Section 3 by analysing some well-known families ofdistance transitive graphs ... iron tablecloth on 5 foot pressWeb1 de ago. de 2010 · A near-polygonal graph is a graph @C which has a set C of m-cycles for some positive integer m such that each 2-path of @C is contained in exactly one cycle in C. If m is the girth of @C then the graph is called polygonal. port st lucie fl homestead applicationWebarc-transitive graphs with vertex stabilizer D8 and order 10752, with 10752 being the smallest order of connected tetravalent half-arc-transitive graphs with vertex stabilizer … iron tables with wood tops