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arXiv · 1810.09954

Sharply $k$-arc-transitive-digraphs: finite and infinite examples

Rögnvaldur G. Möller·Primož Potočnik·Norbert Seifter
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Abstract

A general method for constructing sharply $k$-arc-transitive digraphs, i.e. digraphs that are $k$-arc-transitive but not $(k+1)$-arc-transitive, is presented. Using our method it is possible to construct both finite and infinite examples. The infinite examples can have one, two or infinitely many ends. Among the one-ended examples there are also digraphs that have polynomial growth.

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Rögnvaldur G. Möller, Primož Potočnik, Norbert Seifter. 2018-10-23. Sharply $k$-arc-transitive-digraphs: finite and infinite examples. https://arxiv.org/abs/1810.09954

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