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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 (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.
MSC:
05C40Connectivity
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