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 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 bc(G) for some standard graphs are found and some bounds are obtained. Also, a Nordhaus-Gaddum type result is established.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1026,
author = {V.R. Kulli and B. Janakiram},
title = {The cobondage number of a graph},
journal = {Discussiones Mathematicae Graph Theory},
volume = {16},
year = {1996},
pages = {111-117},
zbl = {0877.05027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1026}
}
V.R. Kulli; B. Janakiram. The cobondage number of a graph. Discussiones Mathematicae Graph Theory, Tome 16 (1996) pp. 111-117. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1026/
[000] [1] E.J. Cockayne and S.T. Hedetniemi, Domination of undirected graphs - A survey, In: Theory and Applications of Graphs (Lecture Notes in Math. 642, Spring-Verlag, 1978) 141-147.
[001] [2] J.F. Fink, M.S. Jakobson, L.F. Kinch and J. Roberts, The bondage number of a graph, Discrete Math. 86 (1990) 47-57, doi: 10.1016/0012-365X(90)90348-L. | Zbl 0745.05056
[002] [3] F. Harary, Graph Theory (Addison-Wesley, Reading Mass., 1969).
[003] [4] E.A. Nordhaus and J.W. Gaddum, On complementary graphs, Amer. Math. Monthly 63 (1956) 175-177, doi: 10.2307/2306658. | Zbl 0070.18503