Strongly regular graphs

A generalization of Wallis-Fon-Der-Flaass construction of strongly regular graphs

“…The parameters of the series S3 coincide with those of the srgs found in [7]. The author didn't find the parameters of the series S1.1, S2, S4, S5 and S6 neither in [4] nor in [9]. They seem to be new.…”

“…The author didn't find these parameters neither in [9] nor in [4]. If n = 2, then all B i are Hadamard designs.…”

“…Therefore ks + r = −k + k , −k + r = s . Together with the equation r (n − 1)(t + 1) + s (n − 1) ( p − t − 1) = −k we obtain a 3 × 3 system of linear equations for k , r , s which yields (9). If ∼ is not a complete graph, then r > s and Spec(A + A(V )) has three distinct eigenvalues if and only if…”

“…After substitution of these values into (9) we obtain that these equations hold iff s = t − 1, that is iff L is an affine plane of order t.…”

Projections of quadrics in finite projective spaces of odd characteristic

“…If q = 3, then the point graph of HT n is a strongly regular graph, also when n is odd. More precisely, it is the strongly regular graph C.10' of Hubaut [16]. There are some constructions of partial geometries and semipartial geometries (for the definitions, see Bose [2] and Debroey, Thas [6]) which have these strongly regular graphs as point graphs, see Thas [19], Hirschfeld and Thas [13] and Delanote [7].…”