Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21281220161201Twin minus domination in directed graphs1491641357510.22049/cco.2016.13575ENMaryamAtapourDepartment of Mathematics
Faculty of basic sciences
University of Bonab
Bonab, Iran, Po. Box: 5551761167AbdollahKhodkarDepartment of Mathematics
University of West Georgia
Carrollton, GA 30118, USAJournal Article20160209Let $D=(V,A)$ be a finite simple directed graph. A function $f:Vlongrightarrow {-1,0,1}$ is called a twin minus dominating function if $f(N^-[v])ge 1$ and $f(N^+[v])ge 1$ for each vertex $vin V$. 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.http://comb-opt.azaruniv.ac.ir/article_13575_b0af46e588dfc0fa0951f816023dd6df.pdf