Combinatorica

, Volume 13, Issue 4, pp 377–396

Infinite highly arc transitive digraphs and universal covering digraphs

  • Peter J. Cameron
  • Cheryl E. Praeger
  • Nicholas C. Wormald
Article

DOI: 10.1007/BF01303511

Cite this article as:
Cameron, P.J., Praeger, C.E. & Wormald, N.C. Combinatorica (1993) 13: 377. doi:10.1007/BF01303511

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.

AMS subject classification code (1991)

05 C 25

Copyright information

© Akadémiai Kiadó 1993

Authors and Affiliations

  • Peter J. Cameron
    • 1
  • Cheryl E. Praeger
    • 3
  • Nicholas C. Wormald
    • 2
  1. 1.School of Mathematical SciencesQueen Mary and Westfield CollegeLondonUK
  2. 2.Department of MathematicsUniversity of MelbourneParkvilleAustralia
  3. 3.Department of MathematicsUniversity of Western AustraliaNedlandsAustralia