Minimal, vertex minimal and commonality minimal CN-dominating graphs

Abstract

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.

Keywords

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