We discuss two ways to determine, given I ⊂ S, whether I ∈ I. The first method is based on the previous lecture, where we considered the set Ŝ = ∪̇Ŝi, a union of disjoint copies of the Si. Formally, we write Ŝ = {(e, i) : e ∈ Si}. There is a natural mapping f : Ŝ → ∪Si which maps (e, i) to e. We can now define a partition matroid Mp over the ground set Ŝ, where I(Mp) = { I ⊆ Ŝ s.t. ∀e ∈ S : |I ∩...

In this paper we will look at the relationship between the intersection number c2 and its diameter for a distance-regular graph. And also, we give some tools to show that a distance-regular graph with large c2 is bipartite, and a tool to show that if kD is too small then the distance-regular graph has to be antipodal.