兰州理工大学学报

兰州理工大学学报 ›› 2022, Vol. 48 ›› Issue (1): 150-155.

• 数理科学 • 上一篇    下一篇

一类含有两个(n－1)-圈的三色有向图本原指数

罗美金*, 卢钰松, 韦玉程   

  1. 河池学院 数理学院, 广西 宜州 546300
  • 收稿日期:2020-05-15 出版日期:2022-02-28 发布日期:2022-03-09
  • 通讯作者: 罗美金(1981-),女,江西广丰人,教授.Email:meijin322@163.com
  • 基金资助:
    国家自然科学基金(31702049),广西教育厅项目(2021JGZ152),广西高校中青年教师科研基础能力提升项目(2019KY0628)

Primitive exponents of a class of three-colored digraphs with two (n－1)-cycles

LUO Mei-jin, LU Yu-song, WEI Yu-cheng   

  1. School of Mathematics and Physics, Hechi University, Yizhou 546300, China
  • Received:2020-05-15 Online:2022-02-28 Published:2022-03-09

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摘要： 为研究非负矩阵簇的本原指数问题,将双色有向图推广到三色有向图.利用有向图与矩阵的对应关系,研究了一类三色有向图,它的未着色图中包含n个顶点,一个n-圈和两个(n－1)-圈,给出了本原条件,指数上界,并对达到指数上界的极图进行了刻画.

关键词: 三色, 有向图, 本原条件, 本原指数

Abstract: In order to study the primitive exponent problem of nonnegative matrix pairs, the two-colored digraphs are extended to three-colored digraphs. Using the corresponding relation between a digraph and a matrix, a class of primitive three-colored digraphs whose uncolored digraphs has n vertices, consists of one n-cycle and two (n－1)-cycles is studied. Some primitive conditions, a tight upper bound of primitive exponents and the characterization of extremal three-colored digraphs are given.

Key words: three-colored, digraph, primitive condition, primitive exponent

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