Geodesic
Graphs without induced P₅ and C₅
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 3, pp. 503-507

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Zverovich [Discuss. Math. Graph Theory 23 (2003), 159-162.] has proved that the domination number and connected domination number are equal on all connected graphs without induced P₅ and C₅. Here we show (with an independent proof) that the following stronger result is also valid: Every P₅-free and C₅-free connected graph contains a minimum-size dominating set that induces a complete subgraph.
Keywords: graph domination, connected domination, complete subgraph, forbidden induced subgraph, characterization 
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Bacsó, Gabor; Tuza, Zsolt. Graphs without induced P₅ and C₅. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 3, pp. 503-507. http://geodesic.mathdoc.fr/item/DMGT_2004_24_3_a12/