Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 9 2 2024 06 01 Independence Number and Connectivity of Maximal Connected Domination Vertex Critical Graphs 185 196 14648 10.22049/cco.2023.28629.1639 EN Norah Almalki Department of Mathematics and Statistics, College of Science, Taif University, Saudi Arabia Pawaton Kaemawichanurat Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology, Thonburi, Thailand Mathematics and Statistics with Applications (MaSA), Bangkok, Thailand Journal Article 2023 05 03 A $k$-CEC graph is a graph $G$ which has connected domination number $\gamma_{c}(G) = k$ and $\gamma_{c}(G + uv) < k$ for every $uv \in E(\overline{G})$. A $k$-CVC graph $G$ is a $2$-connected graph with  $\gamma_{c}(G) = k$ and $\gamma_{c}(G - v) < k$ for any $v \in V(G)$. A graph is said to be maximal $k$-CVC if it is both $k$-CEC and $k$-CVC. Let $\delta$, $\kappa$, and $\alpha$ be the minimum degree, connectivity, and independence number of $G$, respectively. In this work, we prove that for a maximal $3$-CVC graph, if $\alpha = \kappa$, then $\kappa = \delta$. We additionally consider the class of maximal $3$-CVC graphs with $\alpha < \kappa$ and $\kappa < \delta$, and prove that every $3$-connected maximal $3$-CVC graph when $\kappa < \delta$ is Hamiltonian connected. https://comb-opt.azaruniv.ac.ir/article_14648_7cd24310710b75753fe7ac54c88501b3.pdf