Upper Bounds of Exponent of a Class of Two-Colored Digraphs with Three Cycles

罗美金; 高玉斌; 孙权宸

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Upper Bounds of Exponent of a Class of Two-Colored Digraphs with Three Cycles

更新时间：2026-09-14

- Upper Bounds of Exponent of a Class of Two-Colored Digraphs with Three Cycles
- 一类含有三个圈的双色有向图本原指数上界
- Vol. 33, Issue 6, Pages: 627-631(2012)
- 作者机构：
  
  1. 河池学院数学系
  2. 中北大学理学院
  3. 中南大学数学与统计学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2012
- 稿件说明：
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罗美金, 高玉斌, 孙权宸. Upper Bounds of Exponent of a Class of Two-Colored Digraphs with Three Cycles[J]. 2012, 33(6): 627-631.
DOI：

罗美金, 高玉斌, 孙权宸. Upper Bounds of Exponent of a Class of Two-Colored Digraphs with Three Cycles[J]. 2012, 33(6): 627-631. DOI：

摘要

一个双色有向图D是本原的

如果存在非负整数h和k

且h+k0

使得D中的每一对顶点(i

j)都存在从i到j的(h

k)-途径

则称h+k的最小值为D的本原指数.考虑了一类含有三个圈的双色有向图

它的未着色图有n个顶点

包含一个n-圈和两个(n-2)-圈.给出了本原条件和指数上界

并对极图进行了刻划.

Abstract

A two-colored digraphs D is primitive if there exist nonnegative integers h and k with h+k0 such that for each pair (i

j) of vertices there exists an(h

k)-walk in D from i to j.The exponent of the primitive two-colored digraph D is the minimum value of h+k taken over all such h and k.It was considered that the special two-colored digraphs with three cycles whose uncolored digraph has n and consists of one n-cycle and two(n-2)-cycles.Some primitive conditions and a upper bound on the exponents was given.And the characterizations of two-colored extremal digraphs were given.

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references

Shader B L.Exponents of nonnegative matrix pairs[J].Linear Algebra Appl.,2003,363:275-293.

罗美金,高玉斌.一类双色有向图的本原指数[J].中北大学学报,2008,29(2):95.Luo Meijin,Gao Yubin.Primitive exponents of aclass of two-colored digraphs[J].Journal of NorthUniversity of China,2008,29(2):95.(in Chinese)

Gao Yubin,Shao Yanling.Exponent of two-coloreddouble directed cycles[J].Journal of Natural Scienceof Heilongjiang University,2004,4:55-58.

Gao Yubin.Exponent of two-colored digraphs withtwo cycles[J].Linear Algebra Appl.,2005,407:263.

Shao Yanling,Gao Yubin,Sun Liang.Exponent of aclass of two-colored digraphs[J].Linear andMultilinear Algrbra,2005,53(3):175-188.

罗美金.一类含有两个圈的双色有向图本原指数[J].中北大学学报,2007,28(5):377.Luo Meijin.Primitive exponents of a class of two-colored digraphs with two cycles[J].J.of NorthUniv.of China,2007,28(5):377.(in Chinese)

罗美金.一类恰含三个圈的三色有向图的本原指数[J].山东大学学报,2008,43(1):65.Luo Meijin.Primitive exponents of a class of three-colored digraphs with three cycles[J].J.of ShandongUniversity,2008,43(1):65.(in Chinese)

Bai Zhuxiang.Exponents of a class of two-coloreddigraphs[J].Journal of Shanxi University(NaturalScience Edition),2007,30(1):19-23.

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Primitive Exponent of a Class of Two-Colored Digraphs with Two Cycles

A Upper Bound on the Exponents of a Class of Two-Colored Digraphs

Upper Bound on Primitive Exponents of Two-Colored Digraphs with Two Cycles

一类双圈双色有向图的本原指数

一类双色有向图的指数

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