On Restrained Strong Resolving Domination in Graphs

Helyn Cosinas Sumaoy, Helen M. Rara

Abstract

A set S ⊆ V (G) is a restrained strong resolving dominating set in G if S is a strong
resolving dominating set in G and S = V (G) or ⟨V (G) \ S⟩ has no isolated vertex. The restrained strong resolving domination number of G, denoted by γrsR(G), is the smallest cardinality of a restrained strong resolving dominating set in G. In this paper, we present characterizations of the restrained strong resolving dominating sets in the join, corona and lexicographic product of two graphs and determine the exact value of the restrained strong resolving domination number of each of these graphs.

Keywords

restrained strong resolving dominating set, restrained strong resolving domination number, join, corona, lexicographic product

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