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In graph theory, Grassmann graphs are a special class of simple graphs defined from systems of subspaces. The vertices of the Grassmann graph Jq 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 -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.
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