The faber-krahn type isoperimetric inequalities for a graph

Atsushi Katsuda, Hajime Urakawa

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper, a graph theoretic analog to the celebrated Faber-Krahn inequality for the first eigenvalue of the Dirichlet problem of the Laplacian for a bounded domain in the Euclidean space is shown. Namely, the optimal estimate of the first eigenvalue of the Dirichlet boundary problem of the combinatorial Laplacian for a graph with boundary is given.

Original languageEnglish
Pages (from-to)267-281
Number of pages15
JournalTohoku Mathematical Journal
Volume51
Issue number2
DOIs
Publication statusPublished - Jan 1 1999
Externally publishedYes

Fingerprint

Isoperimetric Inequality
First Eigenvalue
Dirichlet Problem
Boundary Problem
Graph in graph theory
Euclidean space
Bounded Domain
Analogue
Estimate

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

The faber-krahn type isoperimetric inequalities for a graph. / Katsuda, Atsushi; Urakawa, Hajime.

In: Tohoku Mathematical Journal, Vol. 51, No. 2, 01.01.1999, p. 267-281.

Research output: Contribution to journalArticle

@article{6badc83bdab649b48b7d7498829c5853,
title = "The faber-krahn type isoperimetric inequalities for a graph",
abstract = "In this paper, a graph theoretic analog to the celebrated Faber-Krahn inequality for the first eigenvalue of the Dirichlet problem of the Laplacian for a bounded domain in the Euclidean space is shown. Namely, the optimal estimate of the first eigenvalue of the Dirichlet boundary problem of the combinatorial Laplacian for a graph with boundary is given.",
author = "Atsushi Katsuda and Hajime Urakawa",
year = "1999",
month = "1",
day = "1",
doi = "10.2748/tmj/1178224816",
language = "English",
volume = "51",
pages = "267--281",
journal = "Tohoku Mathematical Journal",
issn = "0040-8735",
publisher = "Tohoku University, Mathematical Institute",
number = "2",

}

TY - JOUR

T1 - The faber-krahn type isoperimetric inequalities for a graph

AU - Katsuda, Atsushi

AU - Urakawa, Hajime

PY - 1999/1/1

Y1 - 1999/1/1

N2 - In this paper, a graph theoretic analog to the celebrated Faber-Krahn inequality for the first eigenvalue of the Dirichlet problem of the Laplacian for a bounded domain in the Euclidean space is shown. Namely, the optimal estimate of the first eigenvalue of the Dirichlet boundary problem of the combinatorial Laplacian for a graph with boundary is given.

AB - In this paper, a graph theoretic analog to the celebrated Faber-Krahn inequality for the first eigenvalue of the Dirichlet problem of the Laplacian for a bounded domain in the Euclidean space is shown. Namely, the optimal estimate of the first eigenvalue of the Dirichlet boundary problem of the combinatorial Laplacian for a graph with boundary is given.

UR - http://www.scopus.com/inward/record.url?scp=0033465442&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033465442&partnerID=8YFLogxK

U2 - 10.2748/tmj/1178224816

DO - 10.2748/tmj/1178224816

M3 - Article

VL - 51

SP - 267

EP - 281

JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

SN - 0040-8735

IS - 2

ER -