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	Nodal domains of eigenvectors for 1-Laplacian on graphs
	Chang, K. C. ; Shao, Sihong ; Zhang, Dong
	2017
关键词	Laplacian Spectral graph theory Nodal domain Multiplicity of eigenvalue Cheeger&apos Oscillatory eigenfunction SPECTRUM s cut
英文摘要	The eigenvectors for graph 1-Laplacian possess some sort of localization property: On one hand, the characteristic function on any nodal domain of an eigenvector is again an eigenvector with the same eigenvalue; on the other hand, one can pack up an eigenvector for a new graph by several fundamental eigencomponents and modules with the same eigenvalue via few special techniques. The Courant nodal domain theorem for graphs is extended to graph 1-Laplacian for strong nodal domains, but for weak nodal domains it is false. The notion of algebraic multiplicity is introduced in order to provide a more precise estimate of the number of independent eigenvectors. A positive answer is given to a question raised in Chang (2016) [3], to confirm that the critical values obtained by the minimax principle may not cover all eigenvalues of graph 1-Laplacian. (C) 2016 Elsevier Inc. All rights reserved.; National Natural Science Foundation of China [11371038, 11421101, 11471025, 61121002, 91330110]; SCI(E); ARTICLE; 529-574; 308
语种	英语
出处	SCI
出版者	ADVANCES IN MATHEMATICS
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/475053]
专题	数学科学学院
推荐引用方式 GB/T 7714	Chang, K. C.,Shao, Sihong,Zhang, Dong. Nodal domains of eigenvectors for 1-Laplacian on graphs. 2017-01-01.

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