Upper bounds on the total domination number

Teresa W. Haynes, Michael A. Henning

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


A total dominating set of a graph G with no isolated vertex is a set 5 of vertices of G such that every vertex is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set in G. In this paper, we present several upper bounds on the total domination number in terms of the minimum degree, diameter, girth and order.

Original languageEnglish
Pages (from-to)243-256
Number of pages14
JournalArs Combinatoria
Publication statusPublished - Apr 2009
Externally publishedYes


  • Diameter
  • Girth
  • Minimum degree
  • Total domination

ASJC Scopus subject areas

  • General Mathematics


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