The minus k-domination numbers in graphs

Document Type: Original paper

Author

Sirjan University of Technology, Sirjan 78137, Iran

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.

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