๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Lower bounds for the eigenvalues of Laplacian matrices

โœ Scribed by Abraham Berman; Xiao-Dong Zhang

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
70 KB
Volume
316
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

โœฆ Synopsis

We give a lower bound for the second smallest eigenvalue of Laplacian matrices in terms of the isoperimetric number of weighted graphs. This is used to obtain an upper bound for the real parts of the nonmaximal eigenvalues of irreducible nonnegative matrices.

๐Ÿ“œ SIMILAR VOLUMES

Two sharp upper bounds for the Laplacian
Two sharp upper bounds for the Laplacian eigenvalues
โœ Xiao-Dong Zhang ๐Ÿ“‚ Article ๐Ÿ“… 2004 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 168 KB

In this paper, we first obtain a sharp upper bound for the eigenvalues of the adjacency matrix of the line graph of a graph. Then this result is used to present a sharp upper bound for the Laplacian eigenvalues. Another sharp upper bound is presented also. Moreover, we determine all extreme graphs w

A lower bound on the eigenvalues of cert
A lower bound on the eigenvalues of certain hamiltonian matrices
โœ G.A. Gallup ๐Ÿ“‚ Article ๐Ÿ“… 1972 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 334 KB

A lower bound is obta~e~ for the ejge~v~~es elf certain matrices arising from the applicatidn of the theory of : the symmetric groups CO the calculation of enegy for n-ekctron systems. .( '. '\_ . ## .f83 With'these defmitions (4) becomes