(untitled) (European Journal of Pure and Applied Mathematics, 2024)
Let G be a connected graph. A function f:V(G)→ {0,1,2} is a convex Roman dominating function (or CvRDF) if every vertex u for which f(u)=0 is adjacent to at least one vertex v for which f(v)=2 and V_1 V_2 is convex. The weight of a convex Roman dominating function f, denoted by ω_G^CvR(f), is given by ω_G^CvR(f)=_v V(G)f(v). The minimum weight of a CvRDF on G, denoted by γ_CvR(G), is called the convex Roman domination number of G. In this paper, we specifically study the concept of convex Roman domination in the corona and edge corona of graphs, complementary prism, lexicographic product, and Cartesian product of graphs.