Infinite primitive and distance transitive directed graphs of finite out-valency

Daniela Amato, David M. Evans

Research output: Contribution to journalArticlepeer-review

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Abstract

We give certain properties which are satisfied by the descendant set of a vertex in an infinite, primitive, distance transitive digraph of finite out-valency and provide a strong structure theory for digraphs satisfying these properties. In particular, we show that there are only countably many possibilities for the isomorphism type of such a descendant set, thereby confirming a conjecture of the first Author. As a partial converse, we show that certain related conditions on a countable digraph are sufficient for it to occur as the descendant set of a primitive, distance transitive digraph.
Original languageEnglish
Pages (from-to)33-50
Number of pages18
JournalJournal of Combinatorial Theory, Series B
Volume114
Early online date31 Mar 2015
DOIs
Publication statusPublished - Sep 2015

Keywords

  • Infinite digraphs
  • Distance transitivity
  • High arc transitivity
  • Primitive groups

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