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  • Homogeneous factorisations of graph products
    Giudici, Michael ...
    A homogeneous factorisation of a digraph ▫$\Gamma$▫ consists of a partition ▫${\mathscr{P}} = \{P_1,...,P_k\}$▫ of the arc set ▫$A\Gamma$▫ and two vertex-transitive subgroups ▫$M \le G \le ... {\mathrm{Aut}}(\Gamma)$▫ such that ▫$M$▫ fixes each ▫$P_i$▫ setwise while ▫$G$▫ leaves ▫$\mathscr{P}$▫ invariant and permutes its parts transitively. Given two graphs ▫$\Gamma_1$▫ and ▫$\Gamma_2$▫ we consider several ways of taking a product of ▫$\Gamma_1$▫ and ▫$\Gamma_2$▫ to form a larger graph, namely the direct product, cartesian product and lexicographic product. We provide many constructions which enable us to lift homogeneous factorisations or certain arc partitions of ▫$\Gamma_1$▫ and ▫$\Gamma_2$▫, to homogeneous factorisations of the various products.
    Vir: Discrete mathematics. - ISSN 0012-365X (Vol. 308, iss. 16, 2008, str. 3652-3667)
    Vrsta gradiva - članek, sestavni del
    Leto - 2008
    Jezik - angleški
    COBISS.SI-ID - 15021145

    Povezava(-e):

    http://dx.doi.org/10.1016/j.disc.2007.07.025

vir: Discrete mathematics. - ISSN 0012-365X (Vol. 308, iss. 16, 2008, str. 3652-3667)
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