A Note on Connected Domination Critical Graphs

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.