Perfect connected-dominant graphs | Zendy

Igor Edmundovich Zverovich | Zendy

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Perfect connected-dominant graphs

Author(s) -

Igor Edmundovich Zverovich

Publication year - 2003

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1192

Subject(s) - combinatorics , distance hereditary graph , mathematics , induced subgraph , dominating set , connected dominating set , connected component , graph , connectivity , graph factorization , vertex connectivity , induced path , factor critical graph , discrete mathematics , line graph , graph power , vertex (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 ∞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.

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