The bondage numbers and efficient dominations of vertex-transitive graphs

Jia Huang, Jun Ming Xu

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

The bondage number of a graph G is the minimum number of edges whose removal results in a graph with larger domination number. A dominating set D is called an efficient dominating set of G if | N- [v] ∩ D | = 1 for every vertex v ∈ V (G). In this paper we establish a tight lower bound for the bondage number of a vertex-transitive graph. We also obtain upper bounds for regular graphs by investigating the relation between the bondage number and the efficient domination. As applications, we determine the bondage number for some circulant graphs and tori by characterizing the existence of efficient dominating sets in these graphs.

Original languageEnglish (US)
Pages (from-to)571-582
Number of pages12
JournalDiscrete Mathematics
Volume308
Issue number4
DOIs
StatePublished - Feb 28 2008

Fingerprint

Bondage number
Vertex-transitive Graph
Domination
Dominating Set
Efficient Set
Graph in graph theory
Circulant Graph
Domination number
Regular Graph
Torus
Lower bound
Upper bound
Vertex of a graph

Keywords

  • Bondage number
  • Efficient dominating set
  • Vertex-transitive graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Cite this

The bondage numbers and efficient dominations of vertex-transitive graphs. / Huang, Jia; Xu, Jun Ming.

In: Discrete Mathematics, Vol. 308, No. 4, 28.02.2008, p. 571-582.

Research output: Contribution to journalArticle

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