(untitled) (European Journal of Pure and Applied Mathematics, 2023)
Let G be a connected graph. A function f:V(G)→ {0,1,2,3} is a double Roman dominating function of G if for each vV(G) with f(v)=0, v has two adjacent vertices u and w for which f(u)=f(w)=2 or v has an adjacent vertex u for which f(u)=3, and for each vV(G) with f(v)=1, v is adjacent to a vertex u for which either f(u)=2 or f(u)=3. The minimum weight ω_G(f)=_vV(G)f(v) of a double Roman dominating function f of G is the double Roman domination number of G. In this paper, we continue the study of double Roman domination introduced and studied by R.A. Beeler et al. in [2]. First, we characterize some double Roman domination numbers with small values in terms of the domination numbers and 2-domination numbers. Then we determine the double Roman domination numbers of the join, corona, complementary prism and lexicographic product of graphs.