George Brooks

activity

20242026

collaborators

4 papers

math.CO2026

On the classification of regular graphs with positive Lin-Lu-Yau curvature

George Brooks, Nathanael Johnson, William Linz +3

We prove several new structural and classification results about $d$ -regular graphs with positive Lin--Lu--Yau (LLY) curvature. We show that any positively curved $d$ -regular graph…

math.CO2026

Generalized Nordhaus--Gaddum Inequalities for Eigenvalues

Sahil Agarwal, Carter Antley, Joseph Aulenbacher +6

For a graph $G$ , let $λ_{1} (G) \geq λ_{2} (G) \geq \dots \geq λ_{n} (G)$ denote the adjacency eigenvalues of $G$ . We investigate the asymptotic maximum of \[ λ_i(G)+λ_j(\overline G) \] for fi…

math.CO2025

Spectral radius and Hamiltonicity of uniform hypergraphs

George Brooks, William Linz, Ruth Luo

Let $n$ and $r$ be integers with $n - 2 \geq r \geq 3$ . We prove that any $r$ -uniform hypergraph $H$ on $n$ vertices with spectral radius $λ (H) > (r - 1 n - 2)$ mu…

math.CO2024

Maximum spectral gaps of graphs

George Brooks, William Linz, Linyuan Lu

The spread of a graph $G$ is the difference $λ_{1} - λ_{n}$ between the largest and smallest eigenvalues of its adjacency matrix. Breen, Riasanovsky, Tait and Urschel recently determin…