Outer-Connected 2-Resolving Hop Domination in Graphs

Let G be a connected graph. A set S subset of V (G) is an outer-connected 2-resolving hop dominating set of G if S is a 2-resolving hop dominating set of G and S = V (G) or the subgraph < V(G)\S > induced by V(G)\S is connected. The outer-connected 2-resolving hop domination number of G, denoted by gamma c2Rh(G) is the smallest cardinality of an outer-connected 2-resolving hop dominating set of G. This study aims to combine the concept of outer-connected hop domination with the 2-resolving hop dominating sets of graphs. The main results generated in this study include the characterization of outer-connected 2-resolving hop dominating sets in the join, corona, edge corona and lexicographic product of graphs, as well as their corresponding bounds or exact values.