Global double Roman domination in graphs

AbstractA double Roman dominating function (DRDF) on a graph G = (V, E) is a function f : V(G) → {0, 1, 2, 3} having the property that if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, and if f(v) = 1, then vertex v must have at least one neighbor w with f(w) ≥ 2. A DRDF f is called a global double Roman dominating function (GDRDF) if f is also a DRDF of the complement of G. The weight of a GDRDF is the sum of its function value over all vertices. The global double Roman domination number of G, denoted by γgdR(G), is the minimum weight of a GDRDF on G. In this paper, we initiate the study of the global double Roman domination number. We obtain some properties of global double Roman domination number.