On Strong Resolving Domination in the Join and Corona of Graphs

Abstract

Let G be a connected graph. A subset S \subseteq V(G) is a strong resolving dominating set of G if S is a dominating set and for every pair of vertices u,v \in V(G), there exists a vertex w \in S such that u \in I_G[v,w] or v \in I_G[u,w]. The smallest cardinality of a strong resolving dominating set of G is called the strong resolving domination number of G. In this paper, we characterize the strong resolving dominating sets in the join and corona of graphs and determine the bounds or exact values of the strong resolving domination number of these graphs.