Infinite highly arc transitive digraphs and universal covering digraphs

Cheryl Praeger, P.J. Cameron, N.C. Wormald

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    39 Citations (Scopus)

    Abstract

    A digraph (that is a directed graph) is said to be highly arc transitive if its automorphism group is transitive on the set of s-arcs for each s greater-than-or-equal-to 0. Several new constructions are given of infinite highly are transitive digraphs. In particular, for DELTA a connected, 1-arc transitive, bipartite digraph, a highly arc transitive digraph DL(DELTA) is constructed and is shown to be a covering digraph for every digraph in a certain class D(DELTA) of connected digraphs. Moreover, if DELTA is locally finite, then DL(DELTA) is a universal covering digraph for D(DELTA). Further constructions of infinite highly arc transitive digraphs are given.
    Original languageEnglish
    Pages (from-to)377-396
    JournalCombinatorica
    Volume13
    DOIs
    Publication statusPublished - 1993

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