In graph theory, Grassmann graphs are a special class of simple graphs defined from systems of subspaces.

The vertices of the Grassmann graph Jq(n, k) are the k-dimensional subspaces of an n-dimensional vector space over a finite field of order q; two vertices are adjacent when their intersection is (k – 1)-dimensional.

Many of the parameters of Grassmann graphs are q-analogs of the parameters of Johnson graphs, and Grassmann graphs have several of the same graph properties as Johnson graphs.

There is a distance-transitive subgroup of

isomorphic to the projective linear group

[citation needed] In fact, unless

{\displaystyle \operatorname {Aut} (J_{q}(n,k))\cong \operatorname {P\Gamma L} (n,q)\times C_{2}}

( n , k ) ) ≅ Sym ⁡ ( [ n

{\displaystyle \operatorname {Aut} (J_{q}(n,k))\cong \operatorname {Sym} ([n]_{q})}

[1] As a consequence of being distance-transitive,

is also distance-regular.

Letting

denote its diameter, the intersection array of