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The generalized q-Kneser graph Kq (n, k, t) for integers k>t>0 and n>2k-t is the graph whose vertices are the k-dimensional subspaces of an n-dimensional Fq-vectorspace with two vertices U₁ and U₂ adjacent if and only if (U₁ U₂) t>0 and n 3k-t+9 is equal to nk-n-tk-t-1.
Klaus Metsch (Sun,) studied this question.