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Recently, Brouwer, Cioab\u{a}, Ihringer and McGinnis obtained some newresults involving the eigenvalues of various graphs coming from associationschemes and posed some conjectures related to the eigenvalues of Grassmanngraphs, bilinear forms graphs and Hermitian forms graphs. In this paper, weprove some of their conjectures.

On the eigenvalues of Grassmann graphs, Bilinear forms graphs and Hermitian forms graphs