Strong Nonsplit domsaturation number of a graph

Abstract

The strong nonsplit domsaturation number of a graph [Formula: see text], [Formula: see text] is the least positive integer [Formula: see text] such that every vertex of [Formula: see text] lies in a strong nonsplit dominating set of cardinality [Formula: see text]. In this paper, we obtain certain bounds for [Formula: see text] and characterize the graphs which attain these bounds.