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 v∈V. 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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References

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Communications in Combinatorics and Optimization
Volume 1, Issue 2 - Serial Number 2
December 2016
Pages 149-164

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