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Arc-transitive cycle decompositions of tetravalent graphs
Štefko 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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