David Martin Venti

Structural analysis of the signless Brouwer conjecture: projection thresholds, extremal families, and the Laplacian–signless gap

We study the signless Brouwer conjecture (Ashraf–Omidi–Tayfeh-Rezaie): the inequality S_k(Q) ≤ m + C(k+1,2) for the sum of the k largest eigenvalues of the signless Laplacian Q = D + A of a graph with m edges, where C(k+1,2) denotes the binomial coefficient (k+1)(k)/2. We develop...