Complementary nil domination number of a graph

Abstract

A set ${S\subseteq V}$ is said to be a complementary nil dominating set of a graph $G$ if it is a dominating set and its complement ${V-S}$ is not a dominating set for $G$. The minimum cardinality of a $cnd$-set is called the complementary nil domination number of $G$ and is denoted by ${\gamma}_{\rm cnd}(G)$. In this paper some results on the complementary nil domination number are obtained.