Spectral Conditions, Degree Sequences, and Graphical Properties

Integrity, tenacity, binding number, and toughness are significant parameters with which to evaluate network vulnerability and stability. However, we hardly use the definitions of these parameters to evaluate directly. According to the methods, concerning the spectral radius, we show sufficient cond...

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Main Authors: Xiao-Min Zhu, Weijun Liu, Xu Yang
Format: Article
Language:English
Published: MDPI AG 2023-10-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/11/20/4264
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author Xiao-Min Zhu
Weijun Liu
Xu Yang
author_facet Xiao-Min Zhu
Weijun Liu
Xu Yang
author_sort Xiao-Min Zhu
collection DOAJ
description Integrity, tenacity, binding number, and toughness are significant parameters with which to evaluate network vulnerability and stability. However, we hardly use the definitions of these parameters to evaluate directly. According to the methods, concerning the spectral radius, we show sufficient conditions for a graph to be <i>k</i>-integral, <i>k</i>-tenacious, <i>k</i>-binding, and <i>k</i>-tough, respectively. In this way, the vulnerability and stability of networks can be easier to characterize in the future.
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spelling doaj.art-7fc734a5a65c4812a68243391bf32aef2023-11-19T17:13:31ZengMDPI AGMathematics2227-73902023-10-011120426410.3390/math11204264Spectral Conditions, Degree Sequences, and Graphical PropertiesXiao-Min Zhu0Weijun Liu1Xu Yang2College of Sciences, Shanghai Institute of Technology, Shanghai 201418, ChinaCollege of General Education, Guangdong University of Science and Technology, Dongguan 523083, ChinaSchool of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, ChinaIntegrity, tenacity, binding number, and toughness are significant parameters with which to evaluate network vulnerability and stability. However, we hardly use the definitions of these parameters to evaluate directly. According to the methods, concerning the spectral radius, we show sufficient conditions for a graph to be <i>k</i>-integral, <i>k</i>-tenacious, <i>k</i>-binding, and <i>k</i>-tough, respectively. In this way, the vulnerability and stability of networks can be easier to characterize in the future.https://www.mdpi.com/2227-7390/11/20/4264spectral radiusvulnerabilityintegritytenacitybinding numbertoughness
spellingShingle Xiao-Min Zhu
Weijun Liu
Xu Yang
Spectral Conditions, Degree Sequences, and Graphical Properties
Mathematics
spectral radius
vulnerability
integrity
tenacity
binding number
toughness
title Spectral Conditions, Degree Sequences, and Graphical Properties
title_full Spectral Conditions, Degree Sequences, and Graphical Properties
title_fullStr Spectral Conditions, Degree Sequences, and Graphical Properties
title_full_unstemmed Spectral Conditions, Degree Sequences, and Graphical Properties
title_short Spectral Conditions, Degree Sequences, and Graphical Properties
title_sort spectral conditions degree sequences and graphical properties
topic spectral radius
vulnerability
integrity
tenacity
binding number
toughness
url https://www.mdpi.com/2227-7390/11/20/4264
work_keys_str_mv AT xiaominzhu spectralconditionsdegreesequencesandgraphicalproperties
AT weijunliu spectralconditionsdegreesequencesandgraphicalproperties
AT xuyang spectralconditionsdegreesequencesandgraphicalproperties