DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

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Discussiones Mathematicae Graph Theory

THE COBONDAGE NUMBER OF A GRAPH

V.R. Kulli and B. Janakiram

Department of Mathematics, Gulbarga University
Gulbarga-585 106, India

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 bc(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.

Keywords: graph, domination number, cobondage number.

1991 Mathematics Subject Classification: 05C.

References

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