Highly-Arc-Transitive and Descendant-Homogeneous Digraphs with Finite Out-Valency

Abstract

We investigate infinite highly-arc-transitive digraphs with two additional properties, property Z and descendant-homogeneity. We show that if D is a highly-arc-transitive descendant-homogeneous digraph with property Z and F is the subdigraph spanned by the descendant sets of a line in D, then F is a locally finite 2-ended digraph with property Z. If, moreover, D has prime out-valency, then there is only one possibility for the subdigraph F. This knowledge is then used to classify the highly-arc-transitive descendant-homogeneous digraphs of prime out-valency with property Z.

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Correspondence to Daniela A. Amato.

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Amato, D.A. Highly-Arc-Transitive and Descendant-Homogeneous Digraphs with Finite Out-Valency. Combinatorica 39, 1203–1223 (2019). https://doi.org/10.1007/s00493-019-3906-6

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  • 05C20
  • 05E18
  • 20B07
  • 20B27