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Title:Arc-transitive cycle decompositions of tetravalent graphs
Authors:Miklavič, Štefko (Author)
Potočnik, Primož (Author)
Wilson, Stephen (Author)
Work type:Not categorized
Tipology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
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.
Keywords:mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps
Year of publishing:2008
Number of pages:str. 1181-1192
Numbering:Vol. 98, no. 6
COBISS_ID:14627417 Link is opened in a new window
Categories:Document is not linked to any category.
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Keywords:matematika, teorija grafov, dekompozicija ciklov, grupa avtomorfizmov


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