Switching of edges in strongly regular graphs. I. A family of partial
difference sets on 100 vertices.
by Leif K. Jørgensen and Mikhail Klin.
Electronic Journal of Combinatorics (http://www.combinatorics.org/
Vol. 10 (2003), #17, 31 pp.
We present 15 new partial difference sets over 4 non-abelian
groups of order 100 and 2 new strongly regular graphs with intransitive
automorphism groups. The strongly regular graphs and corresponding
partial difference sets have the following parameters: (100,22,0,6),
(100,36,14,12), (100,45,20,20), (100,44,18,20). The existence of
strongly regular graphs with the latter set of parameters was an open
question. Our method is based on combination of Galois correspondence
between permutation groups and association schemes, classical Seidel's
switching of edges and essential use of computer algebra packages. As
a by-product, a few new amorphic association schemes with 3 classes on
100 points are discovered.