关于猜想γ（A）≤（m－1）~2＋1

ON CONJECTURE γ(A)≤(m-1)￣2+1

设Ａ是一个非负矩阵，若存在正整数ｋ，使得Ａ~ｋ＞０，则称Ａ为本原矩阵，而上述ｋ的最小者称为Ａ的本原指数，记作γ（Ａ）．设ｍ为Ａ的最小多项式的次数，ｇ为Ａ的伴随有向图的围长，当ｇ≤ｍ－１时，猜想γ（Ａ）≤（ｍ－１）~２＋１成立。

let A be a nonnegative matrix.If there exists a positive integer k such that Ak>0. then A is called primitive matrix.the least k is called the primitive exponent of A. denoted by γ(A).let m be the degree of the minimal polynomial of A. g the girth of the adjoint digraph of A.In this paper,the conjecture γ(A)≤(m-1)￣2+1 holds if g≤m- 1 is holds is proved.