具有强互反性的双圈图的刻画(英文)

王晓芳; 黄琼湘; 陈琳

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具有强互反性的双圈图的刻画(英文)

更新时间：2026-01-21

- 具有强互反性的双圈图的刻画(英文)
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 29, Issue 3, Pages: 278-286(2012)
- 作者机构：
  
  1. 新疆大学数学与系统科学学院
  2. 新疆医科大学医学工程技术学院
- 作者简介：
- 基金信息：
- DOI：
  CLC： O157.5
- Published：2012
- 稿件说明：
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[1]王晓芳,黄琼湘,陈琳.具有强互反性的双圈图的刻画(英文)[J].新疆大学学报(自然科学版),2012,29(03):278-286.

王晓芳, 黄琼湘, 陈琳. 具有强互反性的双圈图的刻画(英文)[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2012, 29(3): 278-286.
[1]王晓芳,黄琼湘,陈琳.具有强互反性的双圈图的刻画(英文)[J].新疆大学学报(自然科学版),2012,29(03):278-286. DOI：

王晓芳, 黄琼湘, 陈琳. 具有强互反性的双圈图的刻画(英文)[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2012, 29(3): 278-286. DOI：

摘要

如果G是一个简单的连通图

A(G)是G的邻接矩阵

A(G)的特征值称为图G的特征值.如果对于G的任意的特征值λ

都有它的倒数1/λ也是G的一个特征值

则称图G具有互反性(R).更进一步

如果对于G的每一个特征值λ

都有λ和1/λ有相同的重数

则称图G具有强互反性(SR).有(SR)性质的树已经被完全刻画了.有(SR)性质的单圈图在理论上被刻画了.本文研究具有(SR)性质的双圈图.得到了一类双圈图具有(SR)性质的一个充要条件

并由此给出了这类双圈图具有(SR)性质的一个无穷类.

Abstract

We consider only simple connected graph.It is said that a graph has property(R)

if G is nonsingular and the reciprocal of each of its eigenvalue is also an eigenvalue of G.Further

if the multiplicity of each eigenvalue equals that of its reciprocal

the graph is said to have property(SR).The tree with property(SR) have been characterized completely. The unicyclic graphs have been characterized in theory.In this paper

the properties of bicyclic graphs with property(SR) is studied.We obtain a necessary and sufficient condition for a class bicyclic graphs with property(SR)

and thus give an infinite class of such bicyclic graphs with property(SR).

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references

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