Perfect connected-dominant graphs
Igor Edmundovich Zverovich · Discussiones Mathematicae Graph Theory · 2003
If D is a dominating set and the induced subgraph G(D) is connected, then D is a connected dominating set. The minimum size of a connected dominating set in G is called connected domination number ∞c(G) of G. A graph G is called a perfect connected-dominant graph if ∞(H) = ∞c(H) for each connected induced subgraph H of G. We prove that a graph is a perfect connected-dominant graph if and only if it contains no induced path P5 and induced cycle C5.