Strong point stable designs

Abstract

A design (incidence structure) D with incidence matrix A is called point stable, if AA^TJ=αJ (J the all-one-matrix, α ∈ ℕ). D is called strong, if D is a connected regular point stable design with two or three eigenvalues. The most important strong designs are the 2-designs, the partial geometric designs, (r,λ)-designs, regular point stable semi partial geometric designs, 2-PBIBD's and strongly regular graphs. The strong designs are characterized as the regular point stable designs whose multigraphs are linear strongly regular. The eigenvalues of strong designs may be expressed in geometrical terms. For any regular point stable design D we determine the “place” of the multigraph of D in the rank classification scheme. The point graph of a strong design with exactly two connection numbers is strongly regular.