The eigenvalues of oppositeness graphs in buildings of spherical type
نویسنده
چکیده
Consider the graph Γ obtained by taking as vertices the flags in a finite building of spherical type defined over Fq, where two flags are adjacent when they are opposite. We show that the squares of the eigenvalues of Γ are powers of q.
منابع مشابه
Simplicity of Modules given by Oppositeness Relations in Spherical Buildings
Oppositeness graphs of a spherical building are generalizations of the classical Kneser graphs. Recently Brouwer [1] has shown that the square of each eigenvalue of the adjacency matrix of an oppositeness graph is a power of q, for buildings of finite groups of Lie type defined over Fq. Here we show that the incidence modules are simple. The essential part of the proof is a result of Carter and...
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