Finite edge-transitive oriented graphs of valency four: a global approach

Cheryl Praeger, Najat Muthana, Ahmad Al-Kenani, Jehan Al-Bar, Pablo Spiga

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    10 Citations (Scopus)
    192 Downloads (Pure)


    We develop a new framework for analysing finite connected, oriented graphs of
    valency four, which admit a vertex-transitive and edge-transitive group of automorphisms preserving the edge orientation. We identify a sub-family of `basic' graphs such that each graph of this type is a normal cover of at least one basic graph. The basic graphs either admit an edge-transitive group of automorphisms that is quasiprimitive or biquasiprimitive on vertices, or admit an (oriented or unoriented) cycle as a normal quotient. We anticipate that each of these additional properties will facilitate effective further analysis, and we demonstrate that this is so for the quasiprimitive basic graphs. Here we obtain strong restrictions on the group involved, and construct several innite families of such graphs which, to our knowledge, are different from any recorded in the literature so far. Several open problems are posed in the paper.
    Original languageEnglish
    Article number#P1.10
    Number of pages10
    JournalThe Electronic Journal of Combinatorics
    Issue number1
    Publication statusPublished - 22 Jan 2016


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