Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21281120160601The minus k-domination numbers in graphs15281353410.22049/cco.2016.13534ENN.DehgardiSirjan University of Technology, Sirjan 78137, IranJournal Article20160311For any integer $kge 1$, a minus $k$-dominating function is a function $f : V rightarrow {-1,0, 1}$ satisfying $sum_{win N[v]} f(w)ge k$ for every $vin V(G)$, where $N(v) ={u in V(G)mid uvin E(G)}$ and $N[v] =N(v)cup {v}$. The minimum of the values of $sum_{vin V(G)}f(v)$, taken over all minus $k$-dominating functions $f$, is called the minus $k$-domination number and is denoted by $gamma^-_{k}(G)$. In this paper, we introduce the study of minus $k$-domination in graphs and present several sharp lower bounds on the minus $k$-domination number for general graphs.http://comb-opt.azaruniv.ac.ir/article_13534_842d7e5cc29617870d3b17a192a370e4.pdf