Global Roman domination in graphs

A Roman dominating function (RDF) on a graph G = (V, E) is defined to be a function f : V -> {0, 1, 2} satisfying the condition that every vertex u for which f (u) = 0 is adjacent to at least one vertex v for which f(v) = 2. A set S subset of V is a global dominating set if S dominates both G and its complement (G) over bar. The global domination number gamma(g) (G) of a graph G is the minimum cardinality of S. We define a global Roman dominating function on a graph G = (V, E) to be a function f : V -> {0, 1, 2} such thatf is an RDF for both G and its complement (G) over bar. The weight of a global Roman dominating function is the value f (V) = Sigma(u is an element of v) f (u)' The minimum weight of a global Roman dominating function on a graph G is called the global Roman domination number of G and denoted by gamma(gR)(G). In this paper, we initiate a study of this parameter. (C) 2015 Elsevier B.V. All rights reserved.