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

Daniela Amato; David M. Evans

doi:10.1016/j.jctb.2015.03.003

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

Daniela Amato, David M. Evans

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	33-50
Number of pages	18
Journal	Journal of Combinatorial Theory, Series B
Volume	114
Early online date	31 Mar 2015
DOIs	https://doi.org/10.1016/j.jctb.2015.03.003
Publication status	Published - Sep 2015

Keywords

Infinite digraphs
Distance transitivity
High arc transitivity
Primitive groups

Access to Document

10.1016/j.jctb.2015.03.003Licence: CC BY

1-s2.0-S0095895615000337-mainFinal published version, 970 KBLicence: CC BY

Cite this

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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.",

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AU - Evans, David M.

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N2 - 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.

AB - 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.

KW - Infinite digraphs

KW - Distance transitivity

KW - High arc transitivity

KW - Primitive groups

U2 - 10.1016/j.jctb.2015.03.003

DO - 10.1016/j.jctb.2015.03.003

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EP - 50

JO - Journal of Combinatorial Theory, Series B

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