Abstract
A two-colored directed digraph D is primitive if and only if there exist nonnegative integers h and k with h+k>0 such that for each pair (i,j) of vertices there is a (h,k)-walk in D from i to j. The exponent of the primitive two-colored digraph D is defined to be the smallest value of h+k over all suchand . With the knowledge of graph theory, a class of two-colored digraphs with two cycles whose uncolored digraph has 3n vertices and consists of one (2n+1)-cycle and one n-cycle is considered.The exponent bound, exponent set and characteristic of extral two-colored digraphs are given.
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