Symmetric cubic graphs with solvable automorphism groups

Y. Feng, Cai-Heng Li, J. Zhou

    Research output: Contribution to journalArticle

    11 Citations (Scopus)


    © 2014 Elsevier Ltd. A cubic graph Γ is G-arc-transitive if G≤Aut(Γ) acts transitively on the set of arcs of Γ, and G-basic if Γ is G-arc-transitive and G has no non-trivial normal subgroup with more than two orbits. Let G be a solvable group. In this paper, we first classify all connected G-basic cubic graphs and determine the group structure for every G. Then, combining covering techniques, we prove that a connected cubic G-arc-transitive graph is either a Cayley graph, or its full automorphism group is of type 22, that is, a 2-regular group with no involution reversing an edge, and has a non-abelian normal subgroup such that the corresponding quotient graph is the complete bipartite graph of order 6.
    Original languageEnglish
    Pages (from-to)1-11
    JournalEuropean Journal of Combinatorics
    Publication statusPublished - 2015

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