Twin minus domination in directed graphs

Document Type : Original paper

Authors

1 Department of Mathematics Faculty of basic sciences University of Bonab Bonab, Iran, Po. Box: 5551761167

2 Department of Mathematics University of West Georgia Carrollton, GA 30118, USA

Abstract

Let D=(V,A) be a finite simple directed graph. A function f:V{1,0,1} is called a twin minus dominating function  if f(N[v])1 and f(N+[v])1 for each vertex vV. The twin minus domination number of D is γ(D)=min{w(f)f is a twin minus dominating function of D}. In this paper, we initiate the study of twin minus domination numbers in digraphs and present some lower bounds for γ(D) in terms of the order, size and maximum and minimum in-degrees and out-degrees.

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