cover

Strongly Regular Graphs

In Jan 2022 the monograph
A. E. Brouwer & H. Van Maldeghem, Strongly Regular Graphs, Cambridge University Press, 2022.
was published. Errata will be collected here.

Preprint PDF.

(Note: this preprint does not have the same page numbers as the published book. Section numbers, theorem numbers, and references numbered 1-750 will remain constant, also when errata are applied.)

Errata

The back cover does not correctly describe the colors in the picture on the front cover: the Shrikhande graph there is purple and green.

In Section 6.1.2 (book p. 156) the fact that binary lexmin codes are linear is attributed to M. R. Best (who noticed this somewhere in the 1970's). The attribution should have been to V. I. Levenshtein (1960).

For Theorem 8.2.1 (book p. 200) the attribution should have been to P. Delsarte, J. M. Goethals & J. J. Seidel, Orthogonal matrices with zero diagonal, II, Canad. J. Math. 23 (1971) 816-832.

Section 11.5 (book pp. 390-391) contains a list of sporadic rank 3 parameter sets. The sets (36,14,4,6), (50,7,0,1), (162,56,10,24), (1408,567,246,216) and (56,10,0,2) from Theorem 11.3.2 (v), (vi), (vii), (x) and Theorem 11.3.3 (iii) should also have been listed.

Addenda

In Section 10.43 (book p. 323) the chromatic number of the O8+(2) graph on 135 vertices was given as lying in 16-18. L. H. Soicher showed that it is 17.

In Section 10.51 (book p. 331) the chromatic number of the M22 graph on 176 vertices was determined by L. H. Soicher, and is 12.

In Section 10.56 (book p. 334) the chromatic number of the M23 graph was determined by L. H. Soicher, and is 15.

In Section 10.82 (book p. 359) no information is given about cocliques. The Hoffman bound is 40. An example of size 37 is known.

In Section 10.84 (book p. 363) it is said that 50 ≤ α ≤ 84 for the distance 1-or-2 graph of the coset graph of the perfect binary Golay code. In fact α ≥ 72. Four nonequivalent 72-cocliques are known (Mogilnykh / Krotov / Jenrich / Brouwer).

In Section 10.87 (book p. 365) it is said that maximal cocliques of size 32 are known. There are also maximal cocliques of size 33.

In Section 10.94 (book p. 376) no information is given about cocliques. Maximum cocliques have size 40, reaching the Hoffman bound. There are several nonequivalent examples; one is invariant under a group 33+3:L3(3).

Thanks

Thanks to Bhaskar Bagchi, Dima Pasechnik, and Hajime Tanaka for pointing out corrigenda.