The Wiener Index of Trees with Given Degree Sequences

The Wiener index is the sum of topological distances between all pairs of vertices in a connected graph such as represents the structural formula of a molecule. Firstly, we investigate some properties of the partially ordered set of all vectors associated with a tree with respect to majorization. Then these results are used to characterize the trees which minimize the Wiener index among all trees with a given degree sequence. Consequently, all extremal trees with the smallest Wiener index are obtained in the sets of all trees of order n with the maximum degree, the leaf number and the matching number respectively.

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