An incidence structure
consists of a set
of points, a set
of lines, and an incidence relation, or set of flags,
It is a (finite) partial geometry if there are integers
such that: A partial geometry with these parameters is denoted by
A partial linear space
is called a semipartial geometry if there are integers
α ≥ 1 , μ
μ = α ( t + 1 )
It can be easily shown that the collinearity graph of such a geometry is strongly regular with parameters
A nice example of such a geometry is obtained by taking the affine points of
and only those lines that intersect the plane at infinity in a point of a fixed Baer subplane; it has parameters
( s , t , α , μ ) = (