Grassmann graph


Grassmann graphs are a special class of simple graphs defined from systems of subspaces. The vertices of the Grassmann graph are the -dimensional subspaces of an -dimensional vector space over a finite field of order ; two vertices are adjacent when their intersection is -dimensional.
Many of the parameters of Grassmann graphs are -analogs of the parameters of Johnson graphs, and Grassmann graphs have several of the same graph properties as Johnson graphs.

Graph-theoretic properties

There is a distance-transitive subgroup of isomorphic to the projective linear group.
In fact, unless or, ; otherwise or respectively.

Intersection array

As a consequence of being distance-transitive, is also distance-regular. Letting denote its diameter, the intersection array of is given by where: