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arXiv · 2208.14821

Distance-transitive digraphs: descendant-homogeneity, property $Z$ and reachability

Daniela A. Amato
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Abstract

We investigate the class of infinite distance-transitive digraphs $D$ of finite out-valency. We show that if $D$ is a weakly descendant-homogeneous in such a class then either (1) $D$ has property $Z$ and the reachability relation is not universal; or (2) $D$ does not have property $Z$, the reachability relation is universal and $D$ 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.

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Daniela A. Amato. 2022-08-31. Distance-transitive digraphs: descendant-homogeneity, property $Z$ and reachability. https://doi.org/10.1016/j.ejc.2022.103597

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