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1.
On domination numbers of graph bundles
Blaž Zmazek, Janez Žerovnik, 2005

Opis: Let ▫$gamma(G)$▫ 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.
Ključne besede: matematika, teorija grafov, kartezični produkt grafov, dominantno število, dominantna množica, grafovski sveženj, mathematics, graph theory, graph bundle, dominating set, domination number, Cartesian product
Objavljeno: 10.07.2015; Ogledov: 491; Prenosov: 52
URL Povezava na celotno besedilo

2.
On connectedness and hamiltonicity of direct graph bundles
Irena Hrastnik Ladinek, Janez Žerovnik, 2012, izvirni znanstveni članek

Opis: A necessary and sufficient condition for connectedness of direct graph bundles where the fibers are cycles is given. It is also proved that all connected direct graph bundles ▫$X=C_stimes^{alpha}C_t$▫ are Hamiltonian.
Ključne besede: direktni produkt grafov, direktni grafovski sveženj, hamiltonski graf, povezan graf, direct graph product, direct graph bundle, Hamiltonian graph, connected graph, reflection, cyclic ▫$ell$▫-shift
Objavljeno: 10.07.2015; Ogledov: 323; Prenosov: 20
URL Povezava na celotno besedilo

3.
Cyclic bundle Hamiltonicity
Irena Hrastnik Ladinek, Janez Žerovnik, 2011

Opis: Cyclic bundle Hamiltonicity ▫$cbH(G)$▫ of a graph ▫$G$▫ is the minimal ▫$n$▫ for which there is an automorphism ▫$alpha$▫ of ▫$G$▫ such that the graph bundle ▫$C_nBox^{alpha} G$▫ is Hamiltonian. We define ▫$nabla (tilde{G}_{alpha})_{min}$▫, an invariant that is related to the maximal vertex degree of spanning trees suitably involving the symmetries of ▫$G$▫ and prove ▫$cbH(G) leq nabla(tilde{G}_{alpha})_{min} leq cbH(G)+1$▫ for any non-trivial connected graph ▫$G$▫.
Ključne besede: kartezični produkt, kartezični grafovski sveženj, hamiltonski graf, Cartesian product, Cartesian graph bundle, Hamiltonian graph
Objavljeno: 10.07.2015; Ogledov: 413; Prenosov: 51
URL Povezava na celotno besedilo

4.
On connectivity and hamiltonicity of direct graph bundles
Irena Hrastnik Ladinek, Janez Žerovnik, 2011

Opis: A necessary and sufficient condition for connectedness of direct graph bundles where the fibers are cycles is given. It is also proved that all connected direct graph bundles ▫$X=C_stimes^{alpha}C_t$▫ are Hamiltonian.
Ključne besede: direktni produkt grafov, direktni grafovski sveženj, hamiltonski graf, povezan graf, direct graph product, Cartesian graph bundle, Hamiltonian graph, connected graph, reflection, cyclic ▫$ell$▫-shift
Objavljeno: 10.07.2015; Ogledov: 260; Prenosov: 11
URL Povezava na celotno besedilo

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