The minus k-domination numbers in graphs

Abstract

For any integer ‎, ‎a minus k-dominating function is a‎function f‎ : ‎V (G) {-1,0‎, ‎1} satisfying w) for every vertex v, ‎where N(v) ={u V(G) | uv E(G)} and N[v] =N(v)cup {v}. ‎The minimum of ‎the values of v)‎, ‎taken over all minus‎k-dominating functions f,‎ is called the minus k-domination‎number and is denoted by $gamma_k^-(G)$ ‎. ‎In this paper‎, ‎we ‎introduce the study of minus k-domination in graphs and we present‎ ‎several sharp lower bounds on the minus k-domination number for general graphs‎.