Convex Roman Dominating Functions on Graphs under some Binary Operations

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 V₁ ∪ V₂ is convex. The weight of a convex Roman dominating function f, denoted by ωGCvR(f), is given by ωGCvR(f)=∑v ∈ V(G)f(v). The minimum weight of a CvRDF on G, denoted by γCvR(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, lexicographicproduct, and Cartesian product of graphs.