(untitled) (European Journal of Pure and Applied Mathematics, 2023)
Let G be a connected graph. A set DV(G) is called a connected outer-hop independent dominating if D is a connected dominating set and V(G) D is a hop independent set in G, respectively. The minimum cardinality of a connected outer-hop independent dominating set in G, denoted by γ_c^ohi(G), is called the connected outer-hop independent domination number of G. In this paper, we introduce and investigated the concept of connected outer-hop independent domination in a graph. We show that the connected outer-hop independent domination number and connected outer-independent domination number of a graph are incomparable. In fact, we find that their absolute difference can be made arbitrarily large. In addition, we characterize connected outer-hop independent dominating sets in graphs under some binary operations. Furthermore, these results are used to give exact values or bounds of the parameter for these graphs.