Distance-Regular Graphs

In 1989 Springer Verlag published

A. E. Brouwer, A. M. Cohen & A. Neumaier, Distance-Regular Graphs, Ergebnisse der Mathematik 3. Folge, Band 18, Springer, Berlin, etc., 1989.
ISBN 3-540-50919-5, 0-387-50919-5.

Current editions have ISBN 978-3-642-74343-6, and Springer also provides an on-line edition with ISBN 978-3-642-74341-2 (even though they do not own the copyright of this text).

Book Errata

(i) Additions and corrections to this book were collected the subsequent few years (say, 1990-1995) in the file "Additions and Corrections" (PostScript, 53 pp.).

(ii) Fréderic Vanhove pointed out a mistake in Theorem 12.1.1. A writeup (PDF) giving the corrected details.

(iii) There is a typo in Proposition 10.7.4 (p. 337) in the formula for pⁱ_jr: the final factor should be (q^|r|−1) instead of (q−1). See also Parameters of Lie geometries.

(iv) Dima Paduchikh and Jack Koolen pointed out that on p. 169, Remark (iii) the restriction `i < d' is needed.

Additions

This book was fairly complete when it came out, but that is long ago, and since then there has been a lot of progress. A survey of later developments is given in

E. R. van Dam, J. H. Koolen & H. Tanaka, Distance-regular graphs, Electr. J. Combin. (2016) #DS22.