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关于代数连通度的一个注记
  • ISSN号：1006-6837
  • 期刊名称：数学研究
  • 时间：2013.6.15
  • 页码：206-208
  • 分类：O157.5[理学—数学;理学—基础数学]
  • 作者机构：[1]华南农业大学数学系,广东广州510642, [2]南京师范大学数学科学学院,江苏南京210046
  • 相关基金：国家自然科学资金（11071088,11201156）; 江苏省普通高校研究生科研创新计划资助项目（CXZZ12-0378）
  • 相关项目：图谱理论中若干问题的研究
作者： 刘木伙|李风|
关键词： 拉普拉斯矩阵, 拉普拉斯特征值, 代数连通度, 联图, Laplacian matrix, Laplacian spectrum, Algebraic connectivity, Join graph
中文摘要：

图G=（V,E）的次小的拉普拉斯特征值称为G的代数连通度,记为α（G）.设δ（G）为G的最小度.Fiedler早在1973年便证明了α（G）≤δ（G）,但他未能给出等号成立的极图刻划.后来,我们在[6]中确定了当δ（G）≤1/2｜V（G）｜时α（G）=δ（G）的充要条件.本文中,我们将确定任意情况下α（G）=δ（G）成立的所有极图.

英文摘要：

The second smallest eigenvalue of the Laplacian matrix of a graph G, best- known as the algebraic connectivity of G, is denoted by α（G）. Let δ（G） be the minimum degree of vertices of G. As early as in 1973, Fiedler had shown that α（G）≤δ（G）, but he could not characterized the extremal graphs for the equality. In the sequel, when α（G） ≤1/2{V（G）}, we determined all the extremal graphs for α（G） = δ（G） in [6]. In this note, all the graphs for which α（G） = δ（G） are identified.

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期刊信息
  • 《数学研究》
  • 主管单位:厦门大学
  • 主办单位:厦门大学数学科学学院 福建省数学会
  • 主编：林群
  • 地址：厦门大学数学系
  • 邮编：361005
  • 邮箱：jmaths@xmu.edu.cn
  • 电话：0592-2580752 21828321
  • 国际标准刊号：ISSN：1006-6837
  • 国内统一刊号：ISSN：35-1177/O1
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘
  • 被引量:1284