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Infinite primitive and distance transitive directed graphs of finite out-valency
- Source :
- J. Combinatorial Theory (B) vol 114 (2015), 33-50
- Publication Year :
- 2014
-
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.<br />Comment: 18 pages
- Subjects :
- Mathematics - Combinatorics
Mathematics - Group Theory
05C20, 05E18, 20B07, 20B15
Subjects
Details
- Database :
- arXiv
- Journal :
- J. Combinatorial Theory (B) vol 114 (2015), 33-50
- Publication Type :
- Report
- Accession number :
- edsarx.1405.2761
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jctb.2015.03.003