On the Roman domination in the lexicographic product of graphsKraner Šumenjak, Tadeja (Avtor) Repolusk, Polona (Avtor) Tepeh, Aleksandra (Avtor) teorija grafovrimska dominacijapopolna dominacijaleksikografski produktgraph theoryRoman dominationtotal dominationlexicographic productA Roman dominating function of a graph ▫$G = (V,E)$▫ is a function ▫$f colon V to {0,1,2}$▫ such that every vertex with ▫$f(v) = 0$▫ is adjacent to some vertex with ▫$f(v) = 2$▫. The Roman domination number of ▫$G$▫ is the minimum of ▫$w(f) = sum_{v in V}f(v)$▫ over all such functions. Using a new concept of the so-called dominating couple we establish the Roman domination number of the lexicographic product of graphs. We also characterize Roman graphs among the lexicographic product of graphs.20122015-07-10 14:46:13Delo ni kategorizirano51429sl