On Connected Co-Independent Hop Domination in Graphs

Sandra Abo Nanding, Helen Rara

Abstract

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.

Keywords

connected co-independent hop dominating set, connected co-independent hop domination number, strictly co-independent set, strictly co-independent number, join, corona, lexicographic product

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