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arXiv · 1811.02995

Infinite arc-transitive and highly-arc-transitive digraphs

Rögnvaldur G. Möller·Primož Potočnik·Norbert Seifter
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Abstract

A detailed description of the structure of two-ended arc-transitive digraphs is given. It is also shown that several sets of conditions, involving such concepts as Property Z, local quasi-primitivity and prime out-valency, imply that an arc-transitive digraph must be highly-arc-transitive. These are then applied to give a complete classification of two-ended highly-arc-transitive digraphs with prime in- and out-valencies.

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Rögnvaldur G. Möller, Primož Potočnik, Norbert Seifter. 2018-11-27. Infinite arc-transitive and highly-arc-transitive digraphs. https://arxiv.org/abs/1811.02995

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