For a graph G = (V;E) with V = V (G) and E = E(G), a Roman f3g- dominating function is a function f : V ! f0; 1; 2; 3g having the property that Pu2NG(v) f(u) 3 if f(v) = 0, and Pu2NG(v) f(u) 2 if f(v) = 1 for every vertex v 2 G. The weight of a Roman f3g-dominating function f is the sum f(V ) = P v2V (G) f(v) and the minimum weight of a Roman f3g-dominating function on G is the Roman f3g-domination number of G, denoted by fR3g(G). We initiate the study of Roman f3g-domination and show its relationship to other parameters of Roman domination and double Roman domination.
