15 research outputs found

    Cubic symmetric graphs of order a small number times a prime or a prime square

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    AbstractA graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. In this paper, the s-regular elementary abelian coverings of the complete bipartite graph K3,3 and the s-regular cyclic or elementary abelian coverings of the complete graph K4 for each s⩾1 are classified when the fibre-preserving automorphism groups act arc-transitively. A new infinite family of cubic 1-regular graphs with girth 12 is found, in which the smallest one has order 2058. As an interesting application, a complete list of pairwise non-isomorphic s-regular cubic graphs of order 4p, 6p, 4p2 or 6p2 is given for each s⩾1 and each prime p

    2-Arc-transitive metacyclic covers of complete graphs

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    Regular covers of complete graphs whose fibre-preserving automorphism groups act 2-arc-transitively are investigated. Such covers have been classified when the covering transformation groups K are cyclic groups Z(d) for an integer d >= 2, metacyclic abelian groups Z(p)(2), or nonmetacyclic abelian groups Z(p)(3) for a prime p (see S.F. Du et al. (1998) [5] for the first two metacyclic group cases and see S.F. Du et al. (2005) [3] for the third nonmetacyclic group case). In this paper, a complete classification is achieved of all such covers when K is any metacyclic group. (C) 2014 Elsevier Inc. All rights reserved.116Ysciescopu

    Abstracts for BIRS Workshop Symmetries of Graphs and Networks

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    Locally 3-arc-transitive regular covers of complete bipartite graphs

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    In this paper, locally 3-arc-transitive regular covers of complete bipartite graphs are studied, and results are obtained that apply to arbitrary covering transformation groups. In particular, methods are obtained for classifying the locally 3-arc transitive graphs with a prescribed covering transformation group, and these results are applied to classify the locally 3-arc-transitive regular covers of complete bipartite graphs with covering transformation group isomorphic to a cyclic group or an elementary abelian group of order p(2)
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