On the maximum spectral radius of connected graphs with a prescribed order and size

2025/03/22 by Damnjanović, Ivan
#05C35 #05C50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.17883

Abstract

The spectral radius of a graph is the largest modulus of an eigenvalue of its adjacency matrix. Let C_{n, e} be the set of all the connected simple graphs with n vertices and n - 1 + e edges. Here, we solve the spectral radius maximization problem on C_{n, e} when e ≤ 130 or n ≥ e + 2 + 13√(e).

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