Extremal distance spectral radius of graphs with fixed size

2025/01/30 by Lin, Hongying, Zhou, Bo
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.18656

Abstract

Let m be a positive integer. Brualdi and Hoffman proposed the problem to determine the (connected) graphs with maximum spectral radius in a given graph class and they posed a conjecture for the class of graphs with given size m. After partial results due to Friedland and Stanley, Rowlinson completely confirmed the conjecture. The distance spectral radius of a connected graph is the largest eigenvalue of its distance matrix. We investigate the problem to determine the connected graphs with minimum distance spectral radius in the class of graphs with size m. Given m, there is exactly one positive integer n such that n-1\choose 2

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