Tetravalent edge-transitive Cayley graphs with odd number of vertices

Cai-Heng Li, Z.P. Lu, H. Zhang

    Research output: Contribution to journalArticle

    41 Citations (Scopus)


    A characterisation is given of edge-transitive Cayley graphs of valency 4 on odd number of vertices. The characterisation is then applied to solve several problems in the area of edge-transitive graphs: answering a question proposed by Xu [Automorphism groups and isomorphisms of Cayley graphs, Discrete Math. 182 (1998) 309-319] regarding normal Cayley graphs; providing a method for constructing edge-transitive graphs of valency 4 with arbitrarily large vertex-stabiliser; constructing and characterising a new family of half-transitive graphs. Also this study leads to a construction of the first family of arc-transitive graphs of valency 4 which are non-Cayley graphs and have a 'nice' isomorphic 2-factorisation. (c) 2005 Elsevier Inc. All rights reserved.
    Original languageEnglish
    Pages (from-to)164-181
    JournalJournal of combinatorial Theory Series B
    Issue number1
    Publication statusPublished - 2006

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