On the D_α spectral radius of non-transmission regular graphs

2024/02/05 by Zengzhao Xu, Xu, Zengzhao, Weige Xi +2
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2402.03404

openalex publication_date 2024/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a connected graph with order n and size m. Let D(G) and Tr(G) be the distance matrix and diagonal matrix with vertex transmissions of G, respectively. For any real α∈[0,1], the generalized distance matrix D_α(G) of G is defined as D_α(G)=αTr(G)+(1-α)D(G). The largest eigenvalue of D_α(G) is called the D_α spectral radius or generalized distance spectral radius of G, denoted by μ_α(G). In this paper, we establish a lower bound on the difference between the maximum vertex transmission and the D_α spectral radius of non-transmission regular graphs, and we also characterize the extremal graphs attaining the bound.

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