Infinite primitive and distance transitive directed graphs of finite out-valency
File(s)
Published version
Author(s)
Amato, D
Evans, DM
Type
Journal Article
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.
Date Issued
2015-03-31
Date Acceptance
2015-03-31
Citation
Journal of Combinatorial Theory Series B, 2015, 114, pp.33-50
ISSN
1096-0902
Publisher
Elsevier
Start Page
33
End Page
50
Journal / Book Title
Journal of Combinatorial Theory Series B
Volume
114
Copyright Statement
© 2015 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
(http://creativecommons.org/licenses/by/4.0/).
License URL
Subjects
Infinite digraphs
Distance transitivity
High arc transitivity
Primitive groups
Publication Status
Published