Geodesic
Generalized connectivity of some total graphs
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 3, pp. 623-640

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We study the generalized $k$-connectivity $\kappa _k(G)$ as introduced by Hager in 1985, as well as the more recently introduced generalized $k$-edge-connectivity $\lambda _k(G)$. We determine the exact value of $\kappa _k(G)$ and $\lambda _k(G)$ for the line graphs and total graphs of trees, unicyclic graphs, and also for complete graphs for the case $k=3$.
DOI : 10.21136/CMJ.2021.0287-19
Classification : 05C05, 05C40, 05C70, 05C75
Keywords: generalized (edge-)connectivity; line graph; total graph; complete graph 
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Li, Yinkui; Mao, Yaping; Wang, Zhao; Wei, Zongtian. Generalized connectivity of some total graphs. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 3, pp. 623-640. doi: 10.21136/CMJ.2021.0287-19

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