# The bondage number of graphs: good and bad vertices

• Volume: 28, Issue: 3, page 453-462
• ISSN: 2083-5892

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## Abstract

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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.

## How to cite

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Vladimir Samodivkin. "The bondage number of graphs: good and bad vertices." Discussiones Mathematicae Graph Theory 28.3 (2008): 453-462. <http://eudml.org/doc/270385>.

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.},
journal = {Discussiones Mathematicae Graph Theory},
language = {eng},
number = {3},
pages = {453-462},
title = {The bondage number of graphs: good and bad vertices},
url = {http://eudml.org/doc/270385},
volume = {28},
year = {2008},
}

TY - JOUR
TI - The bondage number of graphs: good and bad vertices
JO - Discussiones Mathematicae Graph Theory
PY - 2008
VL - 28
IS - 3
SP - 453
EP - 462
AB - 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.
LA - eng
UR - http://eudml.org/doc/270385
ER -

## References

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