The signless Laplacian spectral radius of graphs without trees

Let \(Q(G)=D(G)+A(G)\) be the signless Laplacian matrix of a simple graph of order \(n\), where \(D(G)\) and \(A(G)\) are the degree diagonal matrix and the adjacency matrix of \(G\), respectively. In this paper, we present a sharp upper bound for the signless spectral radius of \(G\) without any tr...

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Bibliographic Details
Published inarXiv.org
Main Authors Ming-Zhu, Chen, Zhao-Ming, Li, Xiao-Dong, Zhang
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 07.09.2022
Subjects
Graphs
Upper bounds
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Summary:Let \(Q(G)=D(G)+A(G)\) be the signless Laplacian matrix of a simple graph of order \(n\), where \(D(G)\) and \(A(G)\) are the degree diagonal matrix and the adjacency matrix of \(G\), respectively. In this paper, we present a sharp upper bound for the signless spectral radius of \(G\) without any tree and characterize all extremal graphs which attain the upper bound, which may be regarded as a spectral extremal version for the famous Erdős-S\'{o}s conjecture.
ISSN:2331-8422