Proof of Brouwers Conjecture (BC) for all graphs with number of vertices n > n_0 assuming that BC holds for n< n_0 for some n_0

Abstract

Assuming that Brouwers Conjecture the upper bound for the sum of t< n largest eigenvalues of Laplacian graph on n vertices true for n <n_0, we prove the Brouwers Conjecture BC for n > n_0 for some fixed n_0