Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-Connected

Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-Connected

Let G be a connected graph with minimum degree δG and vertex-connectivity κG. The graph G is k-connected if κG≥k, maximally connected if κG=δG, and super-connected if every minimum vertex-cut isolates a vertex of minimum degree. In this paper, we present sufficient conditions for a graph with given...

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Main Authors: Zhen-Mu Hong, Zheng-Jiang Xia, Fuyuan Chen, Lutz Volkmann
Format: Article
Language:English
Published: Hindawi-Wiley 2021-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2021/5588146
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spelling doaj-3b8afb12f25143c29b1c5549ca8c33a52021-03-08T02:00:29ZengHindawi-WileyComplexity1099-05262021-01-01202110.1155/2021/5588146Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-ConnectedZhen-Mu Hong0Zheng-Jiang Xia1Fuyuan Chen2Lutz Volkmann3School of FinanceSchool of FinanceInstitute of Statistics and Applied MathematicsLehrstuhl II für MathematikLet G be a connected graph with minimum degree δG and vertex-connectivity κG. The graph G is k-connected if κG≥k, maximally connected if κG=δG, and super-connected if every minimum vertex-cut isolates a vertex of minimum degree. In this paper, we present sufficient conditions for a graph with given minimum degree to be k-connected, maximally connected, or super-connected in terms of the number of edges, the spectral radius of the graph, and its complement, respectively. Analogous results for triangle-free graphs with given minimum degree to be k-connected, maximally connected, or super-connected are also presented.http://dx.doi.org/10.1155/2021/5588146
collection DOAJ
language English
format Article
sources DOAJ
author Zhen-Mu Hong
Zheng-Jiang Xia
Fuyuan Chen
Lutz Volkmann
spellingShingle Zhen-Mu Hong
Zheng-Jiang Xia
Fuyuan Chen
Lutz Volkmann
Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-Connected
Complexity
author_facet Zhen-Mu Hong
Zheng-Jiang Xia
Fuyuan Chen
Lutz Volkmann
author_sort Zhen-Mu Hong
title Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-Connected
title_short Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-Connected
title_full Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-Connected
title_fullStr Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-Connected
title_full_unstemmed Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-Connected
title_sort sufficient conditions for graphs to be k-connected, maximally connected, and super-connected
publisher Hindawi-Wiley
series Complexity
issn 1099-0526
publishDate 2021-01-01
description Let G be a connected graph with minimum degree δG and vertex-connectivity κG. The graph G is k-connected if κG≥k, maximally connected if κG=δG, and super-connected if every minimum vertex-cut isolates a vertex of minimum degree. In this paper, we present sufficient conditions for a graph with given minimum degree to be k-connected, maximally connected, or super-connected in terms of the number of edges, the spectral radius of the graph, and its complement, respectively. Analogous results for triangle-free graphs with given minimum degree to be k-connected, maximally connected, or super-connected are also presented.
url http://dx.doi.org/10.1155/2021/5588146
work_keys_str_mv AT zhenmuhong sufficientconditionsforgraphstobekconnectedmaximallyconnectedandsuperconnected
AT zhengjiangxia sufficientconditionsforgraphstobekconnectedmaximallyconnectedandsuperconnected
AT fuyuanchen sufficientconditionsforgraphstobekconnectedmaximallyconnectedandsuperconnected
AT lutzvolkmann sufficientconditionsforgraphstobekconnectedmaximallyconnectedandsuperconnected
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