The Existence of Graph whose Vertex Set Can be Partitioned into a Fixed Number of Domination Strong Critical Vertex-sets

Weisheng Zhao, Ying Li, Ruizhi Lin

Let $\gamma (G)$ denote the domination number of a graph $G$. A vertex $v\in V(G)$ is called a \emph{critical vertex} of $G$ if $\gamma (G-v)=\gamma (G)-1$. A graph is called \emph{vertex-critical}…