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# Grassmann Graph

The Grassmann graph is defined such that the vertices are the -dimensional subspaces of an -dimensional finite field of order and edges correspond to pairs of vertices whose intersection is -dimensional.

has vertex count , where is a -binomial, and edge count

is isomorphic to .

The graph is related to Kirkman's schoolgirl problem.

Grassmann graphs are distance-transitive and therefore also distance-regular.

Many parameters of are q-analogs of the corresponding parameters of the Johnson graph .

Distance-Regular Graph, Distance-Transitive Graph, Johnson Graph, Kirkman's Schoolgirl Problem

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## References

Brouwer, A. "Grassmann Graphs." http://www.win.tue.nl/~aeb/graphs/Grassmann.html.Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. Distance Regular Graphs. New York: Springer-Verlag, 1989.

## Cite this as:

Weisstein, Eric W. "Grassmann Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GrassmannGraph.html