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  • Arc-transitive cycle decompositions of tetravalent graphs
    Miklavič, Štefko ; Potočnik, Primož, 1971- ; Wilson, Steve, matematik
    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.
    Source: Journal of combinatorial theory. Series B. - ISSN 0095-8956 (Vol. 98, no. 6, 2008, str. 1181-1192)
    Type of material - article, component part
    Publish date - 2008
    Language - english
    COBISS.SI-ID - 14627417

    Link(s):

    http://dx.doi.org/10.1016/j.jctb.2008.01.005
    Repository of University of Primorska - RUP
    DOI

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