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Maximum Zagreb index, minimum hyper-Wiener index and graph connectivity. (English) Zbl 1171.05350
Summary: We show that among all $n$-vertex graphs with edge or vertex connectivity $k$, the graph $G=K_k\vee (K_{1}+K_{n-k-1})$, the join of $K_k$, the complete graph on $k$ vertices, with the disjoint union of $K_{1}$ and $K_{n-k-1}$, is the unique graph with maximum sum of squares of vertex degrees. This graph is also the unique $n$-vertex graph with edge or vertex connectivity $k$ whose hyper-Wiener index is minimum.

Full Text: DOI
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