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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 $G={K}_{k}\vee \left({K}_{1}+{K}_{n-k-1}\right)$, 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.
##### MSC:
 05C40 Connectivity
##### References:
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