A Proof of a Conjecture on the Distance Spectral Radius and Maximum Transmission of Graphs

Let G be a simple connected graph, and D ( G ) be the distance matrix of G . Suppose that D max ( G ) and λ 1 ( 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 ) - λ 1 ( G ) , and characterize the extremal graphs attain...

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Bibliographic Details
Published in:Graphs and combinatorics 2022-04, Vol.38 (2), Article 49
Main Authors: Liu, Lele, Shan, Haiying, He, Changxiang
Format: Article
Language:English
Subjects:
Combinatorics
Engineering Design
Graphs
Lower bounds
Mathematics
Mathematics and Statistics
Original Paper
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Summary:Let G be a simple connected graph, and D ( G ) be the distance matrix of G . Suppose that D max ( G ) and λ 1 ( 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 ) - λ 1 ( G ) , and characterize the extremal graphs attaining the bound. As a corollary, we solve a conjecture posed by Liu, Shu and Xue.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-021-02455-x