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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 G.C.Lee Y.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2017
Journal Title
Bulletin of the Korean Mathematical Society
ISSN
1015-8634JCR Link
Citation
Bulletin of the Korean Mathematical Society vol. 54, no. 2, pp. 507 - 519
Keywords
Cheeger constantCheeger inequalityDistance-regular graphGreen’s functionLaplacianP-polynomial scheme
Publisher
Korean Mathematical Society
Indexed
SCIE; SCOPUS; KCI WOS scopus
Document Type
Article
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 β-Laplacian for some positive real number β. We present some examples of distance-regular graphs, where we compute our upper bound on their Cheeger constants. © 2017 Korean Mathematical Society.
DOI
10.4134/BKMS.b160517
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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