Exponents of a Class of Three-colored Digraphs

严庆; 邵燕灵

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Exponents of a Class of Three-colored Digraphs

更新时间：2026-09-14

- Exponents of a Class of Three-colored Digraphs
- 一类三色有向图的本原指数
- Vol. 30, Issue 6, Pages: 512-517(2009)
- 作者机构：
  
  中北大学理学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2009
- 稿件说明：
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严庆, 邵燕灵. Exponents of a Class of Three-colored Digraphs[J]. 2009, 30(6): 512-517.
DOI：

严庆, 邵燕灵. Exponents of a Class of Three-colored Digraphs[J]. 2009, 30(6): 512-517. DOI：

摘要

一个三色有向图D是本原的

当且仅当存在非负整数h

k和l

且h+k+l0

使得D中的每一对顶点(i

j)都存在从i到j的(h

l)-途径

并称h+k+l的最小值为D的本原指数.研究了一类特殊的三色有向图

其未着色图恰含一个n-圈、一个(n-1)-圈和一个2-圈

研究了该图的本原性

并给出了在一种本原条件下的三色有向图的本原指数.

Abstract

A three-colored digraph D is primitive if and only if there exist nonnegative integers h

k and l with h+k+l0 such that for each pair(i

j) of vertices there exists an(h

l)-walk in D from i to j.The exponent of the primitive three-colored digraph D is the minimum value of h+k+l taken over all such h

k and l.It is considered the special three-colored digraph whose uncolored digraph consists of one n-cycle

one n-1-cycle and one 2-cycle.The primitive conditions are studied

and the exponent for one three-colored primitive digraph is given.

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references

Shader B L,Suwilo S.Exponents ofnonnegative matrix pairs[J].Linear Algebra Appl.,2003(363):275-293.

Gao Y B,Shao Y L.Exponent of two-colored doubledirected cycles[J].Journal of Natural Science of HeilongjiangUniversity,2004(4):55-58.

Shao Y L,Gao Y B,Sun L.Exponent of aclass of two-colored digraphs[J].Linear and Multilinear Algrbra,2005,53(3):175-188.

Gao Yu B,Shao Y L.Exponent of two-colored digraphs with two cycles[J].Linear Algebra Appl.,2005(407).

Fornasini E,Valcher M.Primitivity of positive matrix pairs:algebraic characterization,graph theoretic descrip-tion,and 2D systems interpretation[J].SIAM J.Matrix Anal.Appl.,1998(19):71-88.

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