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  • Wide diameter of Cartesian graph bundles
    Banič, Iztok ; Žerovnik, Janez, 1958-
    Fault tolerance and transmission delay of networks are important concepts in network design. The notions are strongly related to connectivity and diameter of a graph, and have been studied by many ... authors. Wide diameter of a graph combines studying connectivity with the diameter of a graph. Diameter with width ▫$k$▫ of a graph ▫$G$▫, ▫$k$▫-diameter, is defined as the minimum integer ▫$d$▫ for which there exist at least ▫$k$▫ internally disjoint paths of length at most ▫$d$▫ between any two distinct vertices in ▫$G$▫. Denote by ▫${\mathscr D}_c(G)$▫ the ▫$c$▫-diameter of ▫$G$▫ and ▫$\kappa(G)$▫ the connectivity of ▫$G$▫. In the context of computer networks, wide diameters of Cartesian graph products have been recently studied by many authors. Cartesian graph bundles is a class of graphs that is a generalization of the Cartesian graph products. Let ▫$G$▫ be a Cartesian graph bundle with fiber ▫$F$▫ over base ▫$B$▫, ▫$0 < a \le \kappa(F)$▫, and ▫$0 < b \le \kappa(B)$▫. We prove that ▫${\mathscr D}_{a+b}(G) \le {\mathscr D}_a(F) + {\mathscr D}_b(B) + 1$▫. Moreover, if ▫$G$▫ is a graph bundle with fiber ▫$F \ne K_2$▫ over base ▫$B \ne K_2$▫, then ▫${\mathscr D}_{a+b}(G) \le {\mathscr D}_a(F) + {\mathscr D}_b(B)$▫. The bounds are tight.
    Vir: Algebraic and topological graph theory (Str. 1697-1701)
    Vrsta gradiva - prispevek na konferenci
    Leto - 2010
    Jezik - angleški
    COBISS.SI-ID - 17543176

    Povezava(-e):

    http://dx.doi.org/10.1016/j.disc.2009.11.024
    Digitalna knjižnica Univerze v Mariboru – DKUM

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