On the Minus Domination Number of Graphs

Author： Liu Hailong   Sun Liang  

Publisher： Springer Publishing Company

ISSN： 0011-4642

Source： Czechoslovak Mathematical Journal, Vol.54, Iss.4, 2004-12, pp. : 883-887

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Abstract

Let G = (V, E) be a simple graph. A 3-valued function [Equation s10587-004-6437-1_Ieq1.gif] is said to be a minus dominating function if for every vertex [ Equation s10587-004-6437-1_Ieq2.gif] where N[V] is the closed neighborhood of V. The weight of a minus dominating function f on G is [ Equation s10587-004-6437-1_Ieq3.gif] The minus domination number of a graph G, denoted by γ−(G), equals the minimum weight of a minus dominating function on G. In this paper, the following two results are obtained.(1) If G is a bipartite graph of order N, then[ Equation s10587-004-6437-1_eq1.gif](2) For any negative integer k and any positive integer m 3, there exists a graph G with girth m such that γ−(G) ≤ k. Therefore, two open problems about minus domination number are solved.

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