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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2009, Issue 635

Issues

There are only finitely many regular near polygons and geodetic distance-regular graphs with fixed valency

S. Bang
  • Pohang Mathematics Institute and Department of Mathematics, Pusan National University, Geumjeong Gu, Busan 609-735 Republic of Korea. e-mail:
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/ J. H. Koolen / V. Moulton
Published Online: 2009-07-30 | DOI: https://doi.org/10.1515/CRELLE.2009.080

Abstract

In their 1984 book “Algebraic Combinatorics I: Association Schemes”, Bannai and Ito conjectured that there are only finitely many distance-regular graphs with fixed valency at least three. In a series of papers they showed that their conjecture holds for the class of bipartite distance-regular graphs. In this paper we prove that the Bannai-Ito conjecture also holds for the more general class of regular near polygons, and for the class of geodetic distance-regular graphs.

About the article

Received: 2007-07-23

Revised: 2008-05-30

Published Online: 2009-07-30

Published in Print: 2009-10-01


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2009, Issue 635, Pages 213–235, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2009.080.

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[1]
Harvey I. Blau and Robert J. Hein
Communications in Algebra, 2014, Volume 42, Number 3, Page 1022
[2]
Sejeong Bang and J.H. Koolen
European Journal of Combinatorics, 2014, Volume 36, Page 331
[3]
Marc Cámara, Edwin R. van Dam, Jack H. Koolen, and Jongyook Park
Linear Algebra and its Applications, 2013, Volume 439, Number 9, Page 2692
[4]
Jack H. Koolen, Jongyook Park, and Hyonju Yu
Linear Algebra and its Applications, 2011, Volume 434, Number 12, Page 2404
[5]
J.H. Koolen and S. Bang
Journal of Combinatorial Theory, Series B, 2010, Volume 100, Number 6, Page 573

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