# The cobondage number of a graph

Discussiones Mathematicae Graph Theory (1996)

- Volume: 16, Issue: 2, page 111-117
- ISSN: 2083-5892

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topV.R. Kulli, and B. Janakiram. "The cobondage number of a graph." Discussiones Mathematicae Graph Theory 16.2 (1996): 111-117. <http://eudml.org/doc/270364>.

@article{V1996,

abstract = {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 bc(G) for some standard graphs are found and some bounds are obtained. Also, a Nordhaus-Gaddum type result is established.},

author = {V.R. Kulli, B. Janakiram},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph; domination number; cobondage number; dominating set},

language = {eng},

number = {2},

pages = {111-117},

title = {The cobondage number of a graph},

url = {http://eudml.org/doc/270364},

volume = {16},

year = {1996},

}

TY - JOUR

AU - V.R. Kulli

AU - B. Janakiram

TI - The cobondage number of a graph

JO - Discussiones Mathematicae Graph Theory

PY - 1996

VL - 16

IS - 2

SP - 111

EP - 117

AB - 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 bc(G) for some standard graphs are found and some bounds are obtained. Also, a Nordhaus-Gaddum type result is established.

LA - eng

KW - graph; domination number; cobondage number; dominating set

UR - http://eudml.org/doc/270364

ER -

## References

top- [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.
- [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. Zbl0745.05056
- [3] F. Harary, Graph Theory (Addison-Wesley, Reading Mass., 1969).
- [4] E.A. Nordhaus and J.W. Gaddum, On complementary graphs, Amer. Math. Monthly 63 (1956) 175-177, doi: 10.2307/2306658. Zbl0070.18503

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