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AN UPPER BOUND ON THE CHEEGER CONSTANT OF A DISTANCE-REGULAR GRAPH

Title
AN UPPER BOUND ON THE CHEEGER CONSTANT OF A DISTANCE-REGULAR GRAPH
Authors
Kim, Gil ChunLee, Yoonjin
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2017
Journal Title
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
ISSN
1015-8634JCR Link
Citation
vol. 54, no. 2, pp. 507 - 519
Keywords
Green's functionLaplacianP-polynomial schemedistance regular graphCheeger constantCheeger inequality
Publisher
KOREAN MATHEMATICAL SOC
Indexed
SCIE; SCOPUS; KCI WOS
Abstract
We present an upper bound on the Cheeger constant of a distance-regular graph. Recently, the authors found an upper bound on the Cheeger constant of distance-regular graph under a certain restriction in their previous work. Our new bound in the current paper is much better than the previous bound, and it is a general bound with no restriction. We point out that our bound is explicitly computable by using the valencies and the intersection matrix of a distance-regular graph. As a major tool, we use the discrete Green's function, which is defined as the inverse of beta-Laplacian for some positive real number beta. We present some examples of distance-regular graphs, where we compute our upper bound on their Cheeger constants.
DOI
10.4134/BKMS.b160157
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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