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

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

更新时间：2026-09-14

- Upper Bound on Primitive Exponents of Two-Colored Digraphs with Two Cycles
- 双圈双色有向图的本原指数上界
- Vol. 34, Issue 4, Pages: 358-362(2013)
- 作者机构：
  
  河池学院数学系
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2013
- 稿件说明：
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罗美金. Upper Bound on Primitive Exponents of Two-Colored Digraphs with Two Cycles[J]. 2013, 34(4): 358-362.
DOI：

罗美金. Upper Bound on Primitive Exponents of Two-Colored Digraphs with Two Cycles[J]. 2013, 34(4): 358-362. 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.利用圈矩阵和图论的有关知识

考虑双圈双色有向图

它的未着色图中含有(n+m-q)个顶点

包含一个n-圈和一个m-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 digraph D was primitive

if there existed nonnegative integers h and k with h+k0

each pair(i

j) of vertices had a(h

k)-path in D from i to j.The exponent of the primitive two-colored digraph D was defined to be the smallest value of h+k using relevant knowledge of the cycle matrix and graph theory

we considered two-colored digraphs with two cycles whose uncolored digraph had(n+m-q) vertices and consisted of one n-cycle and one m-cycle.Some primitive conditions and a upper bound on the exponents were given.The characterizations of extremal two-colored digraphs were also given.

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references

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

高玉斌,邵燕灵.双色双向图的本原指数[J].黑龙江大学自然科学版学报,2004,21(4):55-58.Gao Yubin,Shao Yanling.Exponent of two-coloreddouble directed cycles[J].Journal of Natural Scienceof Heilongjiang University,2004,21(4):55-58.(inChinese)

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

Gao Yubin,Shao Yanling.Exponent of two-coloreddigraphs with two cycles[J].Linear Algebra Appl.,2005,407:263-276.

罗美金,高玉斌.一类含有两个圈的双色有向图本原指数[J].中北大学学报(自然科学版),2007,28(5):377-382.Luo Meijin,Gao Yubin.Exponents of a class of two-colored digraphs with two cycles[J].Journal of NorthUniversity of China(Natural Science Edition),2007,28(5):377-382.(in Chinese)

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(自然科学版),2008,29(2):95-100.Luo Meijin,Gao Yubin.Exponents of a class of two-colored digraphs[J].Journal of North University ofChina(Natural Science Edition),2008,29(2):95-100.(in Chinese)

罗美金,高玉斌.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(理学版),2008,43(1):65-72.Luo Meijin,Gao Yubin.Exponents of a class of three-colored digraphs with three cycles[J].Journal ofShandong University(Natural Science Edition),2008,43(1):65-72.(in Chinese)

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