Perfect connected-dominant graphs
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 of G. A graph G is called a perfect connected-dominant graph if 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.