A Cheeger inequality of a distance regular graph using Green's function

Gil Chun Kim; Yoonjin Lee

doi:10.1016/j.disc.2013.06.012

A Cheeger inequality of a distance regular graph using Green's function

Gil Chun Kim, Yoonjin Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We give a Cheeger inequality of distance regular graphs in terms of the smallest positive eigenvalue of the Laplacian and a value α_d which is defined using q-numbers. We can approximate α_d with arbitrarily small positive error β. The method is to use a Green's function, which is the inverse of the β-Laplacian.

Original language	English
Pages (from-to)	2337-2347
Number of pages	11
Journal	Discrete Mathematics
Volume	313
Issue number	20
DOIs	https://doi.org/10.1016/j.disc.2013.06.012
State	Published - 2013

Bibliographical note

Funding Information:
The second author was supported by Priority Research Centers Program through the NRF funded by the Ministry of Education, Science and Technology ( 2009-0093827 ) and by the NRF grant funded by the Korea government (MEST) ( 2012-0005432 ).

Keywords

Cheeger constant
Cheeger inequality
Distance regular graph
Green's function
Laplacian
P-polynomial scheme

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10.1016/j.disc.2013.06.012

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abstract = "We give a Cheeger inequality of distance regular graphs in terms of the smallest positive eigenvalue of the Laplacian and a value αd which is defined using q-numbers. We can approximate αd with arbitrarily small positive error β. The method is to use a Green's function, which is the inverse of the β-Laplacian.",

keywords = "Cheeger constant, Cheeger inequality, Distance regular graph, Green's function, Laplacian, P-polynomial scheme",

author = "Kim, {Gil Chun} and Yoonjin Lee",

note = "Funding Information: The second author was supported by Priority Research Centers Program through the NRF funded by the Ministry of Education, Science and Technology ( 2009-0093827 ) and by the NRF grant funded by the Korea government (MEST) ( 2012-0005432 ). ",

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AU - Lee, Yoonjin

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N2 - We give a Cheeger inequality of distance regular graphs in terms of the smallest positive eigenvalue of the Laplacian and a value αd which is defined using q-numbers. We can approximate αd with arbitrarily small positive error β. The method is to use a Green's function, which is the inverse of the β-Laplacian.

AB - We give a Cheeger inequality of distance regular graphs in terms of the smallest positive eigenvalue of the Laplacian and a value αd which is defined using q-numbers. We can approximate αd with arbitrarily small positive error β. The method is to use a Green's function, which is the inverse of the β-Laplacian.

KW - Cheeger constant

KW - Cheeger inequality

KW - Distance regular graph

KW - Green's function

KW - Laplacian

KW - P-polynomial scheme

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DO - 10.1016/j.disc.2013.06.012

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SN - 0012-365X

VL - 313

SP - 2337

EP - 2347

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 20

ER -

A Cheeger inequality of a distance regular graph using Green's function

Abstract

Bibliographical note

Keywords

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