The bondage number of graphs: good and bad vertices

Vladimir Samodivkin

Discussiones Mathematicae Graph Theory, Tome 28 (2008), p. 453-462 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2008-01-01

Zbl 1173.05037

EUDML-ID : urn:eudml:doc:270385

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