Generalized connectivity of some total graphs

We study the generalized k -connectivity κ k ( G ) as introduced by Hager in 1985, as well as the more recently introduced generalized k -edge-connectivity λ k ( G ). We determine the exact value of κ k ( G ) and λ k ( G ) for the line graphs and total graphs of trees, unicyclic graphs, and also for...

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Bibliographic Details
Published in:Czechoslovak mathematical journal 2021-10, Vol.71 (3), p.623-640
Main Authors: Li, Yinkui, Mao, Yaping, Wang, Zhao, Wei, Zongtian
Format: Article
Language:English
Subjects:
Analysis
Connectivity
Convex and Discrete Geometry
Graph theory
Graphs
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
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Summary:We study the generalized k -connectivity κ k ( G ) as introduced by Hager in 1985, as well as the more recently introduced generalized k -edge-connectivity λ k ( G ). We determine the exact value of κ k ( G ) and λ k ( G ) for the line graphs and total graphs of trees, unicyclic graphs, and also for complete graphs for the case k = 3.
ISSN:0011-4642
1572-9141
DOI:10.21136/CMJ.2021.0287-19