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

罗美金; 高玉斌

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

更新时间：2026-09-14

- Primitive Exponent of a Class of Two-Colored Digraphs with Two Cycles
- 一类含有两个圈的双色有向图本原指数
- Issue 5, Pages: 377-382(2007)
- 作者机构：
  
  中北大学数学系
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2007
- 稿件说明：
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罗美金, 高玉斌. Primitive Exponent of a Class of Two-Colored Digraphs with Two Cycles[J]. 2007, (5): 377-382.
DOI：

罗美金, 高玉斌. Primitive Exponent of a Class of Two-Colored Digraphs with Two Cycles[J]. 2007, (5): 377-382. 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.本文考虑了一类特殊的双色有向图

它的未着色图有(m+n)个顶点

包含一个m-圈和一个n-圈

给出了本原条件和指数上界

并对达到指数上界的极图进行了刻划.

Abstract

A two-colored digraph 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 special two-colored digraphs whose uncolored digraph has m+n vertices and consist of one m-cycle and one n-cycle are considered.Some primitive conditions and the upper bound of the exponents are given.The characterizations of extremal two-colored digraphs are also given.

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references

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

Shao Yanling,Gao Yubin,Sun Liang.Exponent of aclass of two-colored digraphs[J].Linear and MultilinearAlgrbra,2005,2(53):175-188.

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

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

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

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 special two-colored digraphs[J].Journal of Taiyuan Universityof Science and Technology,2006,27(6):481-485.(in Chinese)

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Related Author

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Related Institution

河池学院数学系

中北大学理学院

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中北大学仪器与电子学院

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