On a conjecture about the kth lower multiexponentI

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