TY - JOUR
T1 - The faber-krahn type isoperimetric inequalities for a graph
AU - Katsuda, Atsushi
AU - Urakawa, Hajime
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1999
Y1 - 1999
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.
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U2 - 10.2748/tmj/1178224816
DO - 10.2748/tmj/1178224816
M3 - Article
AN - SCOPUS:0033465442
SN - 0040-8735
VL - 51
SP - 267
EP - 281
JO - Tohoku Mathematical Journal
JF - Tohoku Mathematical Journal
IS - 2
ER -