A three-colored digraph D is primitive if and only if there exist nonnegative integers h

k and l with h+k+l0 such that for each pair(i

j) of vertices there exists an(h

k

l)-walk in D from i to j.The exponent of the primitive three-colored digraph D is the minimum value of h+k+l taken over all such h

k and l.The special three-colored digraphs with odd vertices whose uncolored digraph consists of one n-cycle

one(n-2)-cycle and one 2-cycle.The exponent of compact supper bound for one three-colored primitive digraph is given.