Descendants in infinite, primitive, highly arc-transitive digraphs

作者：Amato Daniela^*

来源：Discrete Mathematics, 2010, 310(13-14): 2021-2036.

DOI：10.1016/j.disc.2010.03.014

• Highly arc-transitive digraph
• Primitive automorphism group
• Descendant set

The descendant set desc(alpha) of a vertex alpha in a directed graph (digraph) is the subdigraph on the set of vertices reachable by a directed path from alpha. We investigate desc(alpha) in an infinite highly arc-transitive digraph D with finite out-valency and whose automorphism group is vertex-primitive. We formulate three conditions which the subdigraph desc(alpha) must satisfy and show that a digraph Gamma satisfying our conditions is constructed in a particular way from a certain bipartite digraph Sigma, which we think of as its 'building block'. In particular, Gamma has infinitely many ends. Moreover, we construct a family of infinite (imprimitive) highly arc-transitive digraphs whose descendant sets satisfy our conditions and are not trees.

• 出版日期2010-7-28