The inverse strong nonsplit domination in graphs

Abstract

Let [Formula: see text] be a simple finite and connected graph. A dominating set [Formula: see text] is a strong nonsplit dominating set if the induced subgraph [Formula: see text] is complete. [Formula: see text] is an inverse strong nonsplit dominating set if [Formula: see text] is a strong nonsplit dominating set of [Formula: see text]. The cardinality of minimum inverse strong nonsplit dominating set is the inverse strong nonsplit domination number [Formula: see text]. In this paper, we initiated and introduced a new variant of strong nonsplit dominating set called inverse strong nonsplit dominating set. Also, we obtain the inverse strong nonsplit domination number and bounds of some standard graphs and its complement.