K＿m－非负算子的素性指标

The Index of Primitivity of K_m-Nonnegative Operator

继续文献［５］工作，将非负矩阵的素性指标估计推广到多面体锥上的素性算子。通过对多面体锥上非负算子有向图的引入，讨论了多面体锥上非负算子的有向图Ｇ（Ａ）与Ｋ＿ｍ－不可约算子，Ｋ＿ｍ－素性算子的关系，对非负矩阵素性指标的一些结论进行了推广，主要结果为：若Ａ∈Ⅱ（Ｋ＿ｍ）为素性算子，且Ｇ（Ａ）是强连接的，则对Ａ的素性指标估计有γ（Ａ）≤ｍ＋ｓ（ｍ－２），其中ｓ是Ｇ（Ａ）中最小简单闭路的长度。这样使得文献［１］中结论成为本文的一个特殊情况。

Extend the estimations of the index of primitivity of a nonnegative matrix to aprimitive operator over a polyhedral cone. We introduce the directed graph of K_m-nonnega-tive operator,and discuss the relations among the directed graph,K_m-irreducible operatorand K_M-primitive operator. Our main result is that if A ∈Ⅱ(K_m)is primitive operator,andG(A)is strong connected, hen γ(A)≤(m+s(m-2),where s is the shortest simple circuitin G(A).Thus,the result of dulmage and Mendelsohn is a special case.