A proof of a conjecture on the distance spectral radius and maximum transmission of graphs

2020/08/29 by Lele Liu, Haiying Shan, Liu, Lele +3
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2008.12935

openalex publication_date 2020/08/29 · openalex created_date 2022/07/22 · openalex updated_date 2026/07/28

Abstract

Let G be a simple connected graph, and D(G) be the distance matrix of G. Suppose that D_max(G) and λ₁(G) are the maximum row sum and the spectral radius of D(G), respectively. In this paper, we give a lower bound for D_max(G)-λ₁(G), and characterize the extremal graphs attaining the bound. As a corollary, we solve a conjecture posed by Liu, Shu and Xue.

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