The Faber-Krahn type isoperimetric inequalities for a graph

Authors
Katsuda, A Urakawa, H
Citation
A. Katsuda et H. Urakawa, The Faber-Krahn type isoperimetric inequalities for a graph, TOHOKU MATH, 51(2), 1999, pp. 267-281
Citations number
5
Categorie Soggetti
Mathematics
Journal title
TOHOKU MATHEMATICAL JOURNAL
ISSN journal
00408735 → ACNP
Volume
51
Issue
2
Year of publication
1999
Pages
267 - 281
Database
ISI
SICI code
0040-8735(199906)51:2<267:TFTIIF>2.0.ZU;2-2
Abstract
In this paper. a graph theoretic analog to the celebrated Faber-Krahn inequ ality for the first eigenvalue of the Dirichlet problem of the Laplacian Fo r a bounded domain in the Euclidean space is shown. Namely, the optimal est imate of the first eigenvalue of the Dirichlet boundary problem of the comb inatorial Laplacian for a graph with boundary is given.