Distance-regular (0,alpha)-reguli
We introduce distance-regular (0,alpha)-reguli and show that they give rise to (0,alpha)-geometries with a distance-regular point graph. This generalises the SPG-reguli of Thas [14] and the strongly regular (alpha,beta)-reguli of Hamilton and Mathon [9], which yield semipartial geometries and strongly regular (alpha,beta)-geometries, respectively. We describe two infinite classes of examples, one of which is a generalisation of the well-known semipartial geometry T-n*(B) arising from a Baer subspace PG(n, q) in PG(n, q(2)).
semipartial geometries distance-regular graphs