# The minus k-domination numbers in graphs

Document Type : Original paper

Author

Sirjan University of Technology, Sirjan 78137, Iran

Abstract

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.

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