An infinite family of sharply two-arc transitive digraphs

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Abstract

We disclaim Conjecture 1 posed by Seifter in [N. Seifter, Transitive digraphs with more than one end, Discrete Math., to appear], that stated that a connected locally finite digraph with more than one end is either 0-, 1- or highly arc transitive. We describe in this work an infinite family of 2-arc transitive two-ended digraphs, that are not 3-arc transitive.

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Work supported partly by the Spanish Research Council (Comisión Interministerial de Ciencia y Tecnología) under the project MTM2005-08990-C02-01.

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