Geodesic
The bondage number of graphs: good and bad vertices
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 3, pp. 453-462

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The domination number γ(G) of a graph G is the minimum number of vertices in a set D such that every vertex of the graph is either in D or is adjacent to a member of D. Any dominating set D of a graph G with |D| = γ(G) is called a γ-set of G. A vertex x of a graph G is called: (i) γ-good if x belongs to some γ-set and (ii) γ-bad if x belongs to no γ-set. The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater then γ(G). In this paper we present new sharp upper bounds for b(G) in terms of γ-good and γ-bad vertices of G.
Keywords: bondage number, γ-bad/good vertex 
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     title = {The bondage number of graphs: good and bad vertices},
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Samodivkin, Vladimir. The bondage number of graphs: good and bad vertices. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 3, pp. 453-462. http://geodesic.mathdoc.fr/item/DMGT_2008_28_3_a5/