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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Format: | Article |
Language: | English |
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MDPI AG
2023-10-01
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Series: | Mathematics |
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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. |
first_indexed | 2024-03-10T21:04:48Z |
format | Article |
id | doaj.art-7fc734a5a65c4812a68243391bf32aef |
institution | Directory Open Access Journal |
issn | 2227-7390 |
language | English |
last_indexed | 2024-03-10T21:04:48Z |
publishDate | 2023-10-01 |
publisher | MDPI AG |
record_format | Article |
series | Mathematics |
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 |