一类含有n-3条公共弧的三色有向图本原指数上界  

Upper Bound of Exponent of a Class of Primitive Three-Colored Digraphs with n-3 Common Arcs

作　　者：罗美金 侯宗毅 LUO Meijin;HOU Zongyi(School of Mathematics and Statistics, Hechi University, Yizhou Guangxi 546300, Chin)

机构地区：[1]河池学院数学与统计学院,广西宜州546300

出　　处：《重庆师范大学学报（自然科学版）》2018年第3期118-123,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11561019);广西壮族自治区教育厅高校科学技术研究项目(No.YB2014335;No.KY2015ZD103)

摘　　要：【目的】在传统单个非负矩阵的基础上,将非负本原矩阵对指数推广到非负本原矩阵簇指数。【方法】根据非负本原矩阵簇与之伴随有向图的一一对应关系,借助三色有向图解决一类非负矩阵簇本原指数问题。【结果】研究了一类三色有向图,它的未着色图中包含n个顶点,1个n-圈、1个(n-1)-圈和1个(n-2)-圈,且3圈有1条长为n-3的公共弧,给出了本原条件,并找到了指数上界。【结论】所得结果有助于一般情形下的非负矩阵簇本原指数问题的研究。[Purposes]On the basis of the traditional single nonnegative matrix,the exponent of nonnegative primitive matrix pairs is extended to the exponent of nonnegative primitive tuples. [Methods]Using a one-to-one relationship between nonnegative primitive matrix tuples and the associated directed digraph of nonnegative matrix tuples,the problem of primitive exponent of nonnegative matrix tuples can be transformed into three-colored digraphs. [Findings]A class of primitive three-colored digraphs with three cycles whose uncolored digraph has n vertices,consists of one n-cycle,one（ n-1）-cycle and one（ n-2）-cycle,and there is a common arc which is n-3 in length on three cycles.Some primitive conditions and the tight upper bound of primitive exponents are given. [Conclusions]The results are helpful to the study of the exponent of nonnegative primitive tuples in the general case.

关 键 词：本原 三色 有向图 指数 上界 

分 类 号：O157.5[理学—数学]