Discussiones Mathematicae Graph Theory 23(1) (2003) 159-162
doi: 10.7151/dmgt.1192

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PERFECT CONNECTED-DOMINANT GRAPHS

Igor Edmundovich Zverovich

RUTCOR, Rutgers University
640 Bartholomew Rd., Piscataway, NJ 08854 USA
e-mail: igor@rutgers.rutcor.edu

Abstract

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 γc(G) of G. A graph G is called a perfect connected-dominant graph if γ(H) = γc(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.

Keywords: Connected domination, perfect connected-dominant graph.

2000 Mathematics Subject Classification: 05C69.

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Received 16 August 2001