On α-total domination in graphs

Michael A. Henning, Nader Jafari Rad

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Let G=(V,E) be a graph with no isolated vertex. A subset of vertices S is a total dominating set if every vertex of G is adjacent to some vertex of S. For some α with 0<α≤1, a total dominating set S in G is an α-total dominating set if for every vertex v∈V\S, |N(v)∩S|≥α|N(v)|. The minimum cardinality of an α-total dominating set of G is called the α-total domination number of G. In this paper, we study α-total domination in graphs. We obtain several results and bounds for the α-total domination number of a graph G.

Original languageEnglish
Pages (from-to)1143-1151
Number of pages9
JournalDiscrete Applied Mathematics
Issue number7-8
Publication statusPublished - May 2012


  • Domination
  • Total domination
  • α-domination

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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