Theorems on partitioned matrices revisited and their applications to graph spectra

淡江大學機構典藏 > 理學院 > 數學學系暨研究所 > 期刊論文 > Item 987654321/58803

jsp.display-item.identifier=請使用永久網址來引用或連結此文件: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/58803

题名:	Theorems on partitioned matrices revisited and their applications to graph spectra
作者:	Chang, Ting-Chung;Tam, Bit-Shun;Wu, Shu-Hui
贡献者:	淡江大學數學學系
关键词:	Graph spectra;Neighborhood equivalence class;Block-stochastic matrix;Laplacian;Signless laplacian
日期:	2010-10
上传时间:	2013-06-13 11:24:37 (UTC+8)
出版者:	Philadelphia: Elsevier Inc.
摘要:	Some old results about spectra of partitioned matrices due to Goddard and Schneider or Haynsworth are re-proved. A new result is given for the spectrum of a block-stochastic matrix with the property that each off-diagonal block has equal entries and each diagonal block has equal diagonal entries and equal off-diagonal entries. The result is applied to the study of the spectra of the usual graph matrices by partitioning the vertex set of the graph according to the neighborhood equivalence relation. The concept of a reduced graph matrix is introduced. The question of when n-2 is the second largest signless Laplacian eigenvalue of a connected graph of order n is treated. A recent conjecture posed by Tam, Fan and Zhou on graphs that maximize the signless Laplacian spectral radius over all (not necessarily connected) graphs with given numbers of vertices and edges is refuted. The Laplacian spectrum of a (degree) maximal graph is reconsidered.
關聯:	Linear Algebra and Its Applications 434(2), pp.559-581
DOI:	10.1016/j.laa.2010.09.014
显示于类别:	[數學學系暨研究所] 期刊論文

文件中的档案:

档案	描述	大小	格式	浏览次数
0024-3795_434(2)p559-581.pdf		312Kb	Adobe PDF	154	检视/开启
0024-3795_434(2)p559-581.pdf		312Kb	Adobe PDF	2	检视/开启

在機構典藏中所有的数据项都受到原著作权保护.

TAIR相关文章