Strongly regular graphs, partial geometries and partially balanced designs

QUASI m-CAYLEY STRONGLY REGULAR GRAPHS

“…However, among the other 14 graphs in this family there are six more graphs that are quasi m-Cayley graphs on some cyclic group. In particular, two of the graphs are quasi m-Cayley graphs on a cyclic group C n for each (m, n) ∈ {(4, 6), (6,4), (8,3)}, and four of the graphs are quasi 8-Cayley graphs on a cyclic group C 3 (but are neither quasi 4-Cayley graphs nor 6-Cayley graphs on a cyclic group). The symbols of the graphs that are distinct from the Paley graph P (25) are listed in the appendix (only the symbols with respect to a quasi (4, 6)-semiregular automorphism are given for the two first ones).…”

“…Strongly regular graphs have been extensively studied since their introduction by Bose [4]; in fact, they are one of the most basic association schemes, the ones with two classes. SRGs with certain symmetry properties have been an active topic of research.…”

Projections of quadrics in finite projective spaces of odd characteristic

“…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]. Thas [20] unified and extended these constructions in the concept of SPG-systems.…”

Perp-systems and partial geometries

“…A semipartial geometry with parameters s; t; a; m, which we denote by spgðs; t; a; mÞ, is a partial linear space of order ðs; tÞ such that for all antiflags ðx; LÞ the incidence number aðx; LÞ equals 0 or a constant a ð0 0Þ and such that for any two points which are not collinear, there are m ð> 0Þ points collinear with both points. Partial geometries were introduced by Bose [2] and semipartial geometries by Debroey and Thas [7].…”