20.500.12556/DKUM-51429 On the Roman domination in the lexicographic product of graphs A 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. teorija grafov rimska dominacija popolna dominacija leksikografski produkt graph theory Roman domination total domination lexicographic product true false false Angleški jezik Angleški jezik Delo ni kategorizirano 2015-07-10 14:46:13 2015-07-10 14:46:13 2022-05-30 03:05:48 2019-07-11 07:18:45 2012 0 0 str. 2030-2036 iss. 13-14 Letn. 160 2012 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 25342464 3345708 0166-218X URN:SI:UM:DK:INAOVOTJ http://dx.doi.org/10.1016/j.dam.2012.04.008 1 https://dk.um.si/Dokument.php?lang=slv&id=75989 Fakulteta za kmetijstvo in biosistemske vede 0 0 0