Descendants in highly arc transitive digraphs

  • Authors:

  • Rögnvaldur G. Möller

  • Affiliations:

  • Science Institute, University of Iceland, IS-107 Reykjavik, Iceland

  • Venue:
  • Discrete Mathematics
  • Year:
  • 2002

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Abstract

A digraph is said to be highly arc transitive if its automorphism group acts transitively on the set of s-arcs for all s ≥ 0. The set of descendants of a directed line is defined as the set of all vertices that can be reached by a directed path from some vertex in the line. The structure of the subdigraph in a locally finite highly arc transitive digraph spanned by the set of descendants of a line is described and this knowledge is used to answer a question of Cameron, Praeger and Wormald. In addition another question of Cameron, Praeger and Wormald is settled.