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 $f:V\longrightarrow \{-1,0,1\}$ is called a twin minus dominating function  if $f(N^-[v])\ge 1$ and $f(N^+[v])\ge 1$ for each vertex $v\in V$. The twin minus domination number of $D$ is $\gamma_{-}^*(D)=\min\{w(f)\mid f \mbox{ is a twin minus dominating function of } D\}$. In this paper, we initiate the study of twin minus domination numbers in digraphs and present some lower bounds for $\gamma_{-}^*(D)$ 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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