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A construction of a pair of strongly regular graphs Г and Г′ of type (4−1) from a pair of skew-symmetric association schemes  of order 4−1 is presented. Examples of graphs with the same parameters as Г and Г′, i.e., of type (4−1), were known only if 4−1=, where  is a prime. The first new graph appearing in the series has parameters (, , 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 Г and Г′, thus to prove that Г and Г′ are not rank three graphs if >2.

Skew-symmetric association schemes with two classes and strongly regular graphs of type L 2n?1(4n?1)