(untitled) (European Journal of Pure and Applied Mathematics, 2025)
A set S of vertices of a graph G is a strong (resp. weak) dominating set of G if for every vertex v of G outside of S, there is a vertex u inside of S such that u and v are adjacent and deg_G(v)deg_G(u) (resp. deg_G(v)deg_G(u)). The minimum cardinality of a strong (resp. weak) dominating set is called the strong (resp. weak) domination number of G, and is denoted by γ_s(G) (resp. γ_w(G)). In this paper, we characterize the strong and weak dominating sets of graphs under some binary operations. As a result, we also determine the exact values of or sharp bounds for the corresponding strong and weak domination numbers.