On a conjecture about the kkth lower multiexponent

In this paper, the conjecture about the kkth lower multiexponent f(n,k)f(n,k) proposed by R.A. Brualdi and B. Liu is proved to be true for the following cases: (1) k=n−ik=n−i, where i=2,3,4,5i=2,3,4,5; (2) small nn, where n≤8n≤8; (3) the class of primitive micro-symmetric digraphs of order nn.