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Perfect connected-dominant graphs

Igor Edmundovich Zverovich — 2003

Discussiones Mathematicae Graph Theory

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 $γ_{c} (G)$ of G. A graph G is called a perfect connected-dominant graph if $γ (H) = γ_{c} (H)$ 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.

A note on domatically critical and cocritical graphs

Igor Edmundovich Zverovich; Vadim E. Zverovich — 1991

Czechoslovak Mathematical Journal

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