Minus domination in regular graphs

Jean Dunbar, Stephen Hedetniemi, Michael A. Henning, Alice A. McRae

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


A three-valued function f defined on the vertices of a graph G = (V,E), f : V → {-1,0,1}, is a minus dominating function if the sum of its function values over any closed neighborhood is at least one. That is, for every υ ∈ V, f(N[υ]) ≥ 1, where N[υ] consists of υ and every vertex adjacent to υ. The weight of a minus dominating function is f(V) = Σ f(υ), over all vertices υ ∈ V. The minus domination number of a graph G, denoted γ-(G), equals the minimum weight of a minus dominating function of G. In this note, we establish a sharp lower bound on γ-(G) for regular graphs G.

Original languageEnglish
Pages (from-to)311-312
Number of pages2
JournalDiscrete Mathematics
Issue number1-3
Publication statusPublished - 22 Feb 1996
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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