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Naslov: Wide diameter of Cartesian graph bundles Banič, Iztok (Avtor)Žerovnik, Janez (Avtor) http://dx.doi.org/10.1016/j.disc.2009.11.024 Angleški jezik Neznano () 1.08 - Objavljeni znanstveni prispevek na konferenci FNM - Fakulteta za naravoslovje in matematiko 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. mathematics, graph theory, Cartesian graph products, Cartesian graph bundles, wide diameter 2010 519.17 17543176 0012-365X URN:SI:UM:DK:OLXAAPZ0 1182 61    Ostalo

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Naslov: Discrete Mathematics Discrete math. North-Holland 0012-365X 1118479 ## Sekundarni jezik

Jezik: Angleški jezik matematika, teorija grafov, kartezični grafovski produkti, kartezični grafovski svežnji

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