Total domination in graphs with minimum degree three

Odile Favaron, Michael A. Henning, Christina M. Mynhart, Joël Puech

Research output: Contribution to journalArticlepeer-review

51 Citations (Scopus)

Abstract

A set S of vertices of a graph G is a total dominating set, if every vertex of V(G) is adjacent to some vertex in S. The total domination number of G, denoted by γt(G), is the minimum cardinality of a total dominating set of G. We prove that, if G is a graph of order n with minimum degree at least 3, then γt(G) ≤ 7n/13.

Original languageEnglish
Pages (from-to)9-19
Number of pages11
JournalJournal of Graph Theory
Volume34
Issue number1
DOIs
Publication statusPublished - May 2000
Externally publishedYes

Keywords

  • Bounds
  • Minimum degree three
  • Total domination number

ASJC Scopus subject areas

  • Geometry and Topology

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