A Note on Connected Domination Critical Graphs

Abstract

Let ${\gamma }_c(G)$ denote the connected domination number of the graph $G$. A graph $G$ is said to be connected domination edge critical, or simply ${\gamma }_c$-critical, if ${\gamma }_c(G+e)<{\gamma }_c(G)$ for each edge $e\in E(\overline{G})$. We answer a question posed by Zhao and Cao concerning ${\gamma }_c$-critical graphs with maximum diameter.