Hop Independent J-Domination in Graphs.

Abstract

Let G be a graph with vertex-set and edge-set V(G) and E(G), respectively. Then S \subseteq V(G) is a hop independent J-dominating if S is both a hop independent and J-dominating set of G. The maximum cardinality of a hop independent J-dominating set of G, denoted by \gamma^{hi}_{J}(G) is the hop independent J-domination number of G. In this paper, we initiate the study on hop independent J-domination of a graph. We characterize the hop independent J-dominating sets in some special graphs, join of two graphs, and we derive some bounds or formulas of the said parameter of each of these graphs.