On domination numbers of graph bundlesZmazek, Blaž (Avtor) Žerovnik, Janez (Avtor) matematikateorija grafovkartezični produkt grafovdominantno številodominantna množicagrafovski sveženjmathematicsgraph theorygraph bundledominating setdomination numberCartesian productLet ▫$gamma(G)$▫ be the domination number of a graph ▫$G$▫. It is shown that for any ▫$k ge 0$▫ there exists a Cartesian graph bundle ▫$B Box_varphi F$▫ such that ▫$gamma(B Box_varphi F) = gamma(B)gamma(F) - 2k$▫. The domination numbers of Cartesian bundles of two cycles are determined exactly when the fibre graph is a triangle or a square. A statement similar to Vizing's conjecture on strong graph bundles is shown not to be true by proving the inequality ▫$gamma(B boxtimes_varphi F) le gamma(B)gamma(F)$▫ for strong graph bundles. Examples of graphs ▫$B$▫ and ▫$F$▫ with ▫$gamma(B boxtimes_varphi F) < gamma(B)gamma(F)$▫ are given.20052015-07-10 12:00:27Delo ni kategorizirano49374sl