TY - JOUR ID - 13534 TI - The minus k-domination numbers in graphs JO - Communications in Combinatorics and Optimization JA - CCO LA - en SN - 2538-2128 AU - Dehgardi, N. AD - Sirjan University of Technology, Sirjan 78137, Iran Y1 - 2016 PY - 2016 VL - 1 IS - 1 SP - 15 EP - 28 KW - ‎Minus $k$-dominating function‎ KW - ‎minus‎ $k$-domination number‎ KW - graph DO - 10.22049/cco.2016.13534 N2 - For any integer $k\ge 1$, a minus $k$-dominating function is a function $f : V \rightarrow \{-1,0, 1\}$ satisfying $\sum_{w\in N[v]} f(w)\ge k$ for every $v\in V(G)$, where $N(v) =\{u \in V(G)\mid uv\in E(G)\}$ and $N[v] =N(v)\cup \{v\}$. The minimum of the values of $\sum_{v\in V(G)}f(v)$, 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. UR - http://comb-opt.azaruniv.ac.ir/article_13534.html L1 - http://comb-opt.azaruniv.ac.ir/article_13534_842d7e5cc29617870d3b17a192a370e4.pdf ER -