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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


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


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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