The Index Set of Maximum Density for a Class of Non-symmetric Matrix

In this paper,the author completely determines the index set of maximum density for the class of n order nonsymmetric imprimitive irreducible Boolean matrix with at least one pair of nonzero symmetry entries and whose given period is two. The main results are the following :(ⅰ)if n(3) is even, then Hn={2,3,4,5,...,2n-5,2n-4};(ⅱ)if n(3) is odd, then  Hn={m∶2≤m≤2n-4 and m is even}.