A note on graphs with large girth and small minus domination number

Dunbar et al. (1998) in Ref. [3] introduced the minus domination number γ−(G) of a graph G and two open problems. In this paper, we show that for every negative integer k and positive integer m ⩾ 3, there exists a graph G with girth m and γ− (G) ⩽ k which is a positive answer for the open problem 2 in Ref. [3].