Geodesic
The cobondage number of a graph
Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 2, pp. 111-117.

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A set D of vertices in a graph G = (V,E) is a dominating set of G if every vertex in V-D is adjacent to some vertex in D. The domination number γ(G) of G is the minimum cardinality of a dominating set. We define the cobondage number b_c(G) of G to be the minimum cardinality among the sets of edges X ⊆ P₂(V) - E, where P₂(V) = X ⊆ V:|X| = 2 such that γ(G+X) γ(G). In this paper, the exact values of b_c(G) for some standard graphs are found and some bounds are obtained. Also, a Nordhaus-Gaddum type result is established.
Keywords: graph, domination number, cobondage number 
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Kulli, V.; Janakiram, B. The cobondage number of a graph. Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 2, pp. 111-117. http://geodesic.mathdoc.fr/item/DMGT_1996_16_2_a1/

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