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arxiv: 1811.02995 · v2 · pith:ZQSIEXMHnew · submitted 2018-11-07 · 🧮 math.CO

Infinite arc-transitive and highly-arc-transitive digraphs

R\"ognvaldur G. M\"oller (1) , Primo\v{z} Poto\v{c}nik (2) , Norbert Seifter (3) ((1) University of Iceland , Reykjav\'ik , Iceland , (2) University of Ljubljana , Ljubljana , Slovenia
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(3) Montanuniversit\"at Leoben Austria)
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classification 🧮 math.CO
keywords arc-transitivedigraphshighly-arc-transitiveprimetwo-endedappliedclassificationcomplete
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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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