Note on conjectures of bondage numbers of planar graphs

Jia Huang, Jun Ming Xu

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The bondage number of a graph G is the cardinality of a smallest set of edges whose removal results in a graph with domination number larger than that of G. The bondage number measures to some extent the robustness of a network with respect to link failure. This note mainly considers some conjectures on the bondage number of a planar graph, and shows limitations of known methods and presents some new approaches to the conjectures by investigating the effects of edge deletion and contraction on the bondage number.

Original languageEnglish (US)
Pages (from-to)3277-3287
Number of pages11
JournalApplied Mathematical Sciences
Volume6
Issue number65-68
StatePublished - Aug 15 2012

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Bondage number
Planar graph
Domination number
Graph in graph theory
Deletion
Contraction
Cardinality
Robustness

Keywords

  • Bondage number
  • Domination
  • Planar graphs

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Note on conjectures of bondage numbers of planar graphs. / Huang, Jia; Xu, Jun Ming.

In: Applied Mathematical Sciences, Vol. 6, No. 65-68, 15.08.2012, p. 3277-3287.

Research output: Contribution to journalArticle

Huang, Jia ; Xu, Jun Ming. / Note on conjectures of bondage numbers of planar graphs. In: Applied Mathematical Sciences. 2012 ; Vol. 6, No. 65-68. pp. 3277-3287.
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