Primitive Exponents of a Class of Two-Colored Digraphs

罗美金; 高玉斌

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Primitive Exponents of a Class of Two-Colored Digraphs

更新时间：2026-09-14

- Primitive Exponents of a Class of Two-Colored Digraphs
- 一类双色有向图的本原指数
- Issue 2, Pages: 95-100(2008)
- 作者机构：
  
  中北大学理学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2008
- 稿件说明：
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罗美金, 高玉斌. Primitive Exponents of a Class of Two-Colored Digraphs[J]. 2008, (2): 95-100.
DOI：

罗美金, 高玉斌. Primitive Exponents of a Class of Two-Colored Digraphs[J]. 2008, (2): 95-100. 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.考虑了一类特殊的双色有向图

它的未着色图含有m+1个顶点

且包含一个m-圈和一个n-圈.给出了某种本原条件和指数上界

并对达到指数最大界的极图进行了刻划.

Abstract

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

there exists an(h

k)-walk in D from i to j.The exponent of the primitive two-colored directed graph D is the minimum value of h+k taken over all such h and k.A class of special two-colored digraphs whose uncolored digraph has m+1 vertices and consists of one m-cycle and one n-cycle are considered.Some primitive conditions and an upper bound on the exponents are presented.The extremal two-colored digraphs are characterized.

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references

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

Gao Yubin,Shao Yanling.Exponent of two-colored doubledirected cycles[J].Journal of Natural Science of Heilong-jiang University,2004(4):55-58.

Shao Yanling,Gao Yubin,Sun Liang.Exponent of a classof two-colored digraphs[J].Linear and Multilinear Al-grbra,2005,53(3):175-188.

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

岳喜尚,高玉斌.一类特殊双色有向图的本原指数[J].太原科技大学学报,2006,27(6):481-485.Yue Xishang,Gao Yubin.Primitive exponent set of a class of special two-colored digraphs[J].Journal of TaiyuanUniversity of Science and Technology,2006,27(6):481-485.(in Chinese)

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