Anwar Saleh Alwardi - University of Mysore
N. D. Soner - University of Mysore

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.

CN-Minimal Dominating (Graph), commonality minimal CN-dominating (graph), vertex minimal CN-dominating (graph)