%0 Journal Article %T Minimal, vertex minimal and commonality minimal CN-dominating graphs %A Anwar Saleh Alwardi %A N. D. Soner %J Transactions on Combinatorics %D 2012 %I University of Isfahan %X We define minimal CN-dominating graph $mathbf {MCN}(G)$, commonality minimal CN-dominating graph $mathbf {CMCN}(G)$ and vertex minimal CN-dominating graph $mathbf {M_{v}CN}(G)$, characterizations are given for graph $G$ for which the newly defined graphs are connected. Further serval new results are developed relating to these graphs. %K CN-Minimal Dominating (Graph) %K commonality minimal CN-dominating (graph) %K vertex minimal CN-dominating (graph) %U http://www.combinatorics.ir/?_action=showPDF&article=497&_ob=907cf6e71495c5344706494bd6c58cf4&fileName=full_text.pdf