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$s$-arc-transitive digraphs

Banff International Research Station for Mathematical Innovation and Discovery

An $s$-arc in a digraph $\Gamma$ is a sequence $v_0,v_1,\ldots,v_s$ of vertices such that for each $i$ the pair $(v_i,v_{i+1})$ is an arc of $\Gamma$. There are several important differences between the study of $s$-arc-transitive graphs and $s$-arc transitive digraphs. For example, there are no 8-arc-transitive graphs of valency at least 8, while for every positive integer $s$ there are infinitely many digraphs of valency at least three that are $s$-arc-transitive but not $(s+1)$-arc transitive. In this talk I will discuss a solution to an old question of Cheryl Praeger about the existence of vertex-primitive 2-arc-transitive digraphs. This is joint work with Cai Heng Li and Binzhou Xia.

Mathematics; Group theory and generalizations; Topological groups, lie groups; Algebraic structures

video/mp4

Author affiliation: The University of Western Australia

2017-05-15

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61681

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/