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Arc-transitive cycle decompositions of tetravalent graphsŠtefko Miklavič,

Primož Potočnik,

Stephen Wilson, 2008, original scientific article

**Abstract:** A cycle decomposition of a graph ▫$\Gamma$▫ is a set ▫$\mathcal{C}$▫ of cycles of ▫$\Gamma$▫ such that every edge of ▫$\Gamma$▫ belongs to exactly one cycle in ▫$\mathcal{C}$▫. Such a decomposition is called arc-transitive if the group of automorphisms of ▫$\Gamma$▫ that preserve setwise acts transitively on the arcs of ▫$\Gamma$▫. 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.

**Found in:** ključnih besedah

**Summary of found:** ...either 2-arc-transitive, or is isomorphic to the medial graph of a reflexible map, or admits...

**Keywords:** mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps

**Published:** 15.10.2013; **Views:** 1458; **Downloads:** 51

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