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About: Brouwer's conjecture     Goto   Sponge   NotDistinct   Permalink

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In the mathematical field of spectral graph theory, Brouwer's conjecture is a conjecture by Andries Brouwer on upper bounds for the intermediate sums of the eigenvalues of the Laplacian of a graph in term of its number of edges. The conjecture states that if G is a simple undirected graph and L(G) its Laplacian matrix, then its eigenvalues λn(L(G)) ≤ λn−1(L(G)) ≤ ... ≤ λ1(L(G)) satisfy where m(G) is the number of edges of G.