Resolving Restrained Domination in Graphs

Gerald Bacon Monsanto, Helen M. Rara

Abstract

Let G be a connected graph. Brigham et al. [3] defined a resolving dominating set
as a set S of vertices of a connected graph G that is both resolving and dominating. A set S ⊆ V (G) is a resolving restrained dominating set of G if S is a resolving dominating set of G and S = V (G) or hV (G) \ Si has no isolated vertex. In this paper, we characterize the resolving restrained dominating sets in the join, corona and lexicographic product of graphs and determine the resolving restrained domination number of these graphs.

Keywords

dominating set, resolving set, resolving dominating set, resolving restrained dominating set, join, corona, lexicographic product

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