Twin minus domination numbers in directed graphs

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.

Abstract licence: CC BY-SA

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