A two-colored directed graph D is primitive if there exist nonnegative integers h and k with h+k0 such that for each pair vertices(i

j) there exists an(h

k)-walk in D from i to j.The exponent of the primitive two-colored directed graph D is the minimum value of h+k taken over all such h and k.A kind of special two-colored directed graph is considered

uncolored graph of which has 2n-1 vertices and consists of four n-cycle and 2n 2-cycle.Some primitive conditions and an upper exponent bound are presented

but the tight upper bound is not given.