On Vizing's conjectureBrešar, Boštjan (Avtor) mathematicsgraph theorygraphCartesian productdomination numberA dominating set ▫$D$▫ gor a graph ▫$G$▫ is a subset ▫$V(G)$▫ such that any vertex in ▫$V(G)-D$▫ has a neighbor in ▫$D$▫, and a domination number ▫$\gamma(G)$▫ is the size of a minimum dominating set for ▫$G$▫. For the Cartesian product ▫$G \Box H$▫ Vizing's conjecture states that ▫$\gamma(G \Box H) \ge \gamma(G)\gamma(H)$▫ for every pair of graphs ▫$G,H$▫. In this paper we introduce a new concept which extends the ordinary domination of graphs, and prove that the conjecture holds when ▫$\gamma(G) = \gamma(H) = 3$▫.20012017-03-31 14:20:00Znanstveno delo65351ISSN: 1234-3099UDK: 519.17OceCobissID: 7487065COBISS_ID: 11010137ISSN pri članku: 1234-3099NUK URN: URN:SI:UM:DK:PXU92DXHsl