Geodesic
Lower bounds for the domination number
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 3, pp. 475-487

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In this note, we prove several lower bounds on the domination number of simple connected graphs. Among these are the following: the domination number is at least two-thirds of the radius of the graph, three times the domination number is at least two more than the number of cut-vertices in the graph, and the domination number of a tree is at least as large as the minimum order of a maximal matching.
Keywords: domination number, radius, matching, cut-vertices 
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Delaviña, Ermelinda; Pepper, Ryan; Waller, Bill. Lower bounds for the domination number. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 3, pp. 475-487. http://geodesic.mathdoc.fr/item/DMGT_2010_30_3_a9/