Vishal Gupta

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20242026

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math.CO2026

A spectral Moore problem and the Yang-Koolen conjecture

Vishal Gupta

We study the maximum order $v (k, θ)$ of a connected $k$ -regular graph whose second largest eigenvalue is at most $θ$ . For every real $θ \geq 1$ , we prove that \[ T(θ) =\limsup_{k\to\i…

math.CO2025

The non-existence of some Moore polygons and spectral Moore bounds

Sebastian M. Cioabă, Vishal Gupta, Hiroshi Nozaki +1

In this paper, we study the maximum order $v (k, θ)$ of a connected $k$ -regular graph whose second largest eigenvalue is at most $θ$ . From Alon-Boppana and Serre, we know that $v(k,θ…

math.CO2024

On the minimum spectral radius of connected graphs of given order and size

Sebastian M. Cioabă, Vishal Gupta, Celso Marques

In this paper, we study a question of Hong from 1993 related to the minimum spectral radii of the adjacency matrices of connected graphs of given order and size. Hong asked if it i…