# The cobondage number of a graph

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

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## Abstract

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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 ${b}_{c}\left(G\right)$ 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.

## How to cite

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V.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

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1. [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. [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
4. [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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