Real and integer domination in graphs

Wayne Goddard, Michael A. Henning

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


For an arbitrary subset ℘ of the reals, we define a function f : V → ℘ to be a ℘-dominating function of graph G = (V,E) if the sum of the function values over any closed neighbourhood is at least 1. That is, for every v ∈ V, f(N(v)∪{v}) ≥ 1. The ℘-domination number of a graph is defined to be the infimum of f(V) taken over all ℘-dominating functions f. When ℘ = {0,1} one obtains the standard domination number. We obtain various theoretical and computational results on the ℘-domination number of a graph.

Original languageEnglish
Pages (from-to)61-75
Number of pages15
JournalDiscrete Mathematics
Issue number1-3
Publication statusPublished - 28 Mar 1999
Externally publishedYes


  • Domination
  • Integer domination
  • Real domination

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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