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ArticleOriginal scientific text

Title

The bondage number of graphs: good and bad vertices

Authors 1

Affiliations

  1. Department of Mathematics, University of Architecture Civil Engineering and Geodesy, Hristo Smirnenski 1 Blv., 1046 Sofia, Bulgaria

Abstract

The domination number γ(G) of a graph G is the minimum number of vertices in a set D such that every vertex of the graph is either in D or is adjacent to a member of D. Any dominating set D of a graph G with |D| = γ(G) is called a γ-set of G. A vertex x of a graph G is called: (i) γ-good if x belongs to some γ-set and (ii) γ-bad if x belongs to no γ-set. The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater then γ(G). In this paper we present new sharp upper bounds for b(G) in terms of γ-good and γ-bad vertices of G.

Keywords

ENG
bondage number, γ-bad/good vertex

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Discussiones Mathematicae Graph Theory
2008/28/3
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Pages:
453-462
Main language of publication
English
Received
2007-09-20
Accepted
2008-07-14
Published
2008

DOI: 10.7151/dmgt.1419

Exact and natural sciences