مشخصات پژوهش

TheRomangamedomination number of an undirected graphG is defined by the following game. Players A and D orient the edges of the graph G alternately, with D playing first, until all edges are oriented. Player D (frequently called Dominator) tries to minimize the Roman domination number of the resulting digraph, while player A (Avoider) tries to maximize it. This game gives a unique number depending only on G, if we suppose that both A and D play according to their optimal strategies. This number is called the Roman game domination number of G and is denoted by γRg(G). In this paper we initiate the study of the Roman game domination number of a graph and we establish some bounds on γRg(G). We also determine the Roman game domination number for some classes of graphs.