Geodesic
Highly connected counterexamples to a conjecture on α-domination
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 435-440

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An infinite class of counterexamples is given to a conjecture of Dahme et al. [1] concerning the minimum size of a dominating vertex set that contains at least a prescribed proportion of the neighbors of each vertex not belonging to the set.
Keywords: graph, dominating set, α-domination 
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Tuza, Zsolt. Highly connected counterexamples to a conjecture on α-domination. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 435-440. http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a19/