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Arc-transitive cycle decompositions of tetravalent graphs

By Štefko Miklavič, Primož Potočnik and Steve Wilson

Abstract

AbstractA cycle decomposition of a graph Γ is a set C of cycles of Γ such that every edge of Γ belongs to exactly one cycle in C. Such a decomposition is called arc-transitive if the group of automorphisms of Γ that preserve C setwise acts transitively on the arcs of Γ. In this paper, we study arc-transitive cycle decompositions of tetravalent graphs. In particular, we are interested in determining and enumerating arc-transitive cycle decompositions admitted by a given arc-transitive tetravalent graph. Among other results we show that a connected tetravalent arc-transitive graph is either 2-arc-transitive, or is isomorphic to the medial graph of a reflexible map, or admits exactly one cycle structure

Publisher: Elsevier Inc.
Year: 2008
DOI identifier: 10.1016/j.jctb.2008.01.005
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