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
$f:Vlongrightarrow {-1,0,1}$ is called a twin minus dominating
function (TMDF) if $f(N^-[v])ge 1$ and $f(N^+[v])ge 1$ for each
vertex $vin V$. The twin minus domination number of $D$ is
$gamma_{-}^*(D)=min{w(f)mid f mbox{ is a TMDF of } D}$. 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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