Skew-symmetric association schemes with two classes and strongly regular graphs of type L 2n-1(4n-1).
Pasechnik, Dmitrii V.
Date of Issue1992
School of Physical and Mathematical Sciences
A construction of a pair of strongly regular graphs Γn and Γ'n of type L 2n-1 (4n-1) from a pair of skew-symmetric association schemes W, W' of order 4n-1 is presented. Examples of graphs with the same parameters as Γn and Γ'n, i.e., of type L 2n-1 (4n-1), were known only if 4n-1 = p^S, where p is a prime. The first new graph appearing in the series has parameters (v, k, λ) = (225, 98, 45). A 4-vertex condition for relations of a skew-symmetric association scheme (very similar to one for the strongly regular graphs) is introduced and is proved to hold in any case. This has allowed us to check the 4-vertex condition for Γn and Γ'n, thus to prove that Γn and Γ'n are not rank three graphs if n > 2.
Acta applicandae mathematicae
© 1992 Kluwer Academic Publishers. This is the author created version of a work that has been peer reviewed and accepted for publication by Acta Applicandae Mathematicae, Kluwer Academic Publishers. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1007/BF00053382].