The minus total k-domination numbers in graphs.

For any integer k ≥ 1 , a minus total k -dominating function is a function f : V (G) → { − 1 , 0 , 1 } satisfying ∑ w ∈ N (v) f (w) ≥ k for every v ∈ V (G) , where N (v) = { u ∈ V (G) | u v ∈ E (G) }. The minimum of the values of ∑ v ∈ V (G) f (v) , taken over all minus total k -dominating functions f , is called the minus total k -domination number and is denoted by γ t k − (G). In this paper, we initiate the study of minus total k -domination in graphs, and we present different sharp bounds on γ t k − (G). In addition, we determine the minus total k -domination number of some classes of graphs. Some of our results are extensions of known properties of the minus total domination number γ t − (G) = γ t 1 − (G). [ABSTRACT FROM AUTHOR]