Distance-transitive digraphs: descendant-homogeneity, property $Z$ and reachability
Combinatorics
2022-09-01 v1
Abstract
We investigate the class of infinite distance-transitive digraphs of finite out-valency. We show that if is a weakly descendant-homogeneous in such a class then either (1) has property and the reachability relation is not universal; or (2) does not have property , the reachability relation is universal and has infinite in-valency. Also, we show that earlier results, proved in the context of highly-arc-transitive digraphs, hold under the weaker condition of distance-transitivity. Finally, we give a description of a subclass of the class distance-transitive weakly descendant-homogeneous digraphs for which the reachability relation is not universal.
Keywords
Cite
@article{arxiv.2208.14821,
title = {Distance-transitive digraphs: descendant-homogeneity, property $Z$ and reachability},
author = {Daniela A. Amato},
journal= {arXiv preprint arXiv:2208.14821},
year = {2022}
}