The spectral radius of minor free graphs

In this paper, we present a sharp upper bound for the spectral radius of an \(n\)-vertex graph without \(F\)-minor for sufficient large \(n\), where \(F\) is obtained from the complete graph \(K_r\) by deleting disjointed paths. Furthermore, the graphs which achieved the sharp bound are characterize...

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Bibliographic Details
Published inarXiv.org
Main Authors Ming-Zhu, Chen, A-Ming, Liu, Xiao-Dong, Zhang
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.11.2023
Subjects
Graph theory
Graphs
Upper bounds
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Summary:In this paper, we present a sharp upper bound for the spectral radius of an \(n\)-vertex graph without \(F\)-minor for sufficient large \(n\), where \(F\) is obtained from the complete graph \(K_r\) by deleting disjointed paths. Furthermore, the graphs which achieved the sharp bound are characterized. This result may be regarded to be an extended revision of the number of edges in an \(n\)-vertex graph without \(F\)-minor.
ISSN:2331-8422