Descendant sets in infinite, primitive highly arc transitive digraphs with prime power out-valency

作者：Amato Daniela^*

来源：Discrete Mathematics, 2018, 341(9): 2529-2534.

DOI：10.1016/j.disc.2018.06.002

• Digraphs
• Descendant sets
• Primitivity
• High arc transitivity

The descendant set desc(alpha) of a vertex a in a directed graph (digraph) is the subdigraph on the set of vertices reachable by a directed path from a. We study the structure of descendant sets Gamma in an infinite, primitive, highly arc transitive digraph with out-valency p(k), where p is a prime and k >= 1. It was already known that Gamma is a tree when k = 1 and we show the same holds when k = 2. However, for k >= 3 there are examples of infinite, primitive highly arc transitive digraphs of out-valency p(k) whose descendant sets are not trees, for some prime p.

• 出版日期2018-9