On Resolving Hop Domination in Graphs

Jerson Saguin Mohamad, Helen M. Rara

Abstract

A set S of vertices in a connected graph G is a resolving hop dominating set of G if S is a resolving set in G and for every vertex v ∈ V (G) \ S there exists u ∈ S such that dG(u, v) = 2. The smallest cardinality of such a set S is called the resolving hop domination number of G. This paper presents the characterizations of the resolving hop dominating sets in the join, corona and lexicographic product of two graphs and determines the exact values of their corresponding resolving hop domination number.

Keywords

resolving hop dominating set, resolving hop domination number, join, corona, lexicograhic product

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