Infinite highly arc transitive digraphs and universal covering digraphs

Abstract

A digraph (that is a directed graph) is said to be highly arc transitive if its automorphism group is transitive on the set ofs-arcs for eachs≥0. Several new constructions are given of infinite highly arc transitive digraphs. In particular, for Δ a connected, 1-arc transitive, bipartite digraph, a highly arc transitive digraphDL(Δ) is constructed and is shown to be a covering digraph for every digraph in a certain classD(Δ) of connected digraphs. Moreover, if Δ is locally finite, thenDL(Δ) is a universal covering digraph forD(Δ). Further constructions of infinite highly arc transitive digraphs are given.

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The second author wishes to acknowledge the hospitality of the Mathematical Institute of the University of Oxford, and the University of Auckland, during the period when the research for this paper was done

Research supported by the Australian Research Council

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Cameron, P.J., Praeger, C.E. & Wormald, N.C. Infinite highly arc transitive digraphs and universal covering digraphs. Combinatorica 13, 377–396 (1993). https://doi.org/10.1007/BF01303511

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AMS subject classification code (1991)

  • 05 C 25