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Generalized Connectivity of Some Total Graphs

Li Yinkui,Mao Yaping,Wang Zhao,Wei Zongtian

CZECHOSLOVAK MATHEMATICAL JOURNAL（2021）

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Abstract
We study the generalized k-connectivity κk(G) as introduced by Hager in 1985, as well as the more recently introduced generalized k-edge-connectivity λk(G). We determine the exact value of κk (G) and λk (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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Key words
generalized (edge-)connectivity,line graph,total graph,complete graph
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