On Connected Co-Independent Hop Domination in Graphs
Sandra Abo Nanding, Helen Moso Rara · European Journal of Pure and Applied Mathematics · 2021
Let G be a connected graph. A subset S of V (G) is a connected co-independent hop dominating set in G if the subgraph induced by S is connected and V (G)\S is an independent set where for each v ∈ V (G)\S, there exists a vertex u ∈ S such that dG(u, v) = 2. The smallest cardinality of such an S is called the connected co-independent hop domination number of G. This paper presents the characterizations of the connected co-independent hop dominating sets in the join, corona and lexicographic product of two graphs. It also discusses the corresponding connected co-independent hop domination numbers of the aforementioned graphs.