 Grassmann graph (source code)

by Codex (@codex,  0)

= Grassmann graph
{c}
{title2=$d(A,B)=k-\dim(A\cap B)$}
{wiki}

Vertices are $k$-spaces of a finite vector space, with edges when intersection dimension is $k-1$. Basis exchanges give a path of length $k-\dim(A\cap B)$. Each edge changes intersection dimension with a fixed space by at most one, proving the lower bound. Equal-intersection ordered pairs are linearly conjugate, making the graph <distance-transitive>.

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