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 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 …
High-girth arc-transitive graphs
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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 … 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 …
WebTETRAVALENT ARC-TRANSITIVE GRAPHS WITH UNBOUNDED VERTEX-STABILIZERS PRIMOŽ POTOCNIK, PABLO SPIGAˇ and GABRIEL VERRET (Received … WebWe prove the existence of vertex transitive trivalent graphs of arbitrarily high girth using Cayley graphs. The same result is proved for symmetric (that is vertex transitive and …
Webarc-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 … Web16 de dez. de 2010 · A further outcome of our analysis is a precise identification of which of these graphs are Cayley. We also investigate higher level of transitivity of the smallest …
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 …
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 … cannon stage lighting baltimoreWebARC–TRANSITIVE NON–CAYLEY GRAPHS FROM REGULAR MAPS P. GVOZDJAK and J. ˇSIR A´Nˇ Abstract. We prove that the underlying graphs of p-gonal r-valent orientably regular maps are arc-transitive but non-Cayley if r≥3 and pis a prime greater than r(r−1). 1. Introduction Orientable maps, i.e., embeddings of graphs in orientable surfaces ... fizzero sparkling whiteWeb3 de out. de 2006 · In fact we will show that every 5-arc-transitive cubic Cayley graph Cay (G, S) is a cover of one of just six such graphs, which are the only examples with G core-free in Aut Cay (G, S). The... fizzers candy rollsWebClearly 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 … fizzero marks and spencerWebinitial 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 cannon stainless steel gimbal mountsWeb1 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 … fizzer cricketWeb1 de mai. de 1989 · Highly Arc Transitive Digraphs. Finite digrahs Г with a group G of automorphisms acting transitively on the set of s -arcs, for some s ⩾ 2, are investigated. For each valency v and each s ⩾ 2 an infinite family of finite digraphs of valency v which are s -arc transitive but not ( s + 1)-arc transitive are constructed. cannon stainless steel mounting base 1903004