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Generalized connectivity of some total graphs

Yinkui LiYaping MaoZhao WangZongtian Wei — 2021

Czechoslovak Mathematical Journal

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 .

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