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.

中文翻译：

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一些总图的广义连通性

我们研究了广义ķ -connectivity κ _ķ（ģ），如通过海格于1985年引入，以及更近期推出广义ķ _edge时的连通λ _ķ（ģ）。我们确定κ _k ( G ) 和λ _k ( G )的准确值，用于树的线图和总图、单环图以及k = 3情况下的完整图。