A upper bound on the exponents of a class of two-colored digraphs

A two-colored digraphs D is primitive if there exist nonnegative integers h and k with h+k>0 such that for each pair (i,j) of vertices there exists an (h,k)-walk in D from i to j. Then the minimum value of h+k is called D of the primitive exponent. The special two-colored digraphs whose uncolored digraph have 2n-t-2 vertices and consist of one n-cycle and one (n-t)-cycle was considered. Some primitive conditions and an upper bound on the exponents were given, and the characterizations of extremal two-colored digraphs were described.