There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k2k and large diameter

Jongyook Park; Jack H. Koolen; Greg Markowsky

doi:10.1016/j.jctb.2013.09.005

There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k2k and large diameter

Jongyook Park
, Jack H. Koolen
, Greg Markowsky

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

3 Scopus citations

Abstract

In this paper, we show that for given positive integer C, there are only finitely many distance-regular graphs with valency k at least three, diameter D at least six and k2/k≤C. This extends a conjecture of Bannai and Ito.

Original language	English
Pages (from-to)	733-741
Number of pages	9
Journal	Journal of Combinatorial Theory. Series B
Volume	103
Issue number	6
DOIs	https://doi.org/10.1016/j.jctb.2013.09.005
State	Published - Nov 2013

Keywords

Bannai-Ito conjecture
Distance-regular graphs

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10.1016/j.jctb.2013.09.005

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title = "There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k2k and large diameter",

abstract = "In this paper, we show that for given positive integer C, there are only finitely many distance-regular graphs with valency k at least three, diameter D at least six and k2/k≤C. This extends a conjecture of Bannai and Ito.",

keywords = "Bannai-Ito conjecture, Distance-regular graphs",

author = "Jongyook Park and Koolen, \{Jack H.\} and Greg Markowsky",

year = "2013",

month = nov,

doi = "10.1016/j.jctb.2013.09.005",

language = "English",

volume = "103",

pages = "733--741",

journal = "Journal of Combinatorial Theory. Series B",

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T1 - There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k2k and large diameter

AU - Park, Jongyook

AU - Koolen, Jack H.

AU - Markowsky, Greg

PY - 2013/11

Y1 - 2013/11

N2 - In this paper, we show that for given positive integer C, there are only finitely many distance-regular graphs with valency k at least three, diameter D at least six and k2/k≤C. This extends a conjecture of Bannai and Ito.

AB - In this paper, we show that for given positive integer C, there are only finitely many distance-regular graphs with valency k at least three, diameter D at least six and k2/k≤C. This extends a conjecture of Bannai and Ito.

KW - Bannai-Ito conjecture

KW - Distance-regular graphs

UR - https://www.scopus.com/pages/publications/84887613333

U2 - 10.1016/j.jctb.2013.09.005

DO - 10.1016/j.jctb.2013.09.005

M3 - Article

AN - SCOPUS:84887613333

SN - 0095-8956

VL - 103

SP - 733

EP - 741

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

IS - 6

ER -

There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k2k and large diameter

Abstract

Keywords

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