Minimizing Wiener Index for Vertex-Weighted Trees with Given Weight and Degree Sequences

Abstract

In 1997 Klavžar and Gutman suggested a generalization of the Wiener index to vertex-weighted graphs. We minimize the Wiener index over the set of trees with the given vertex weights' and degrees' sequences and show an optimal tree to be the, so-called, Huffman tree built in a bottom-up manner by sequentially connecting vertices of the least weights.

2 figures

References in corpus (1)

• Minimizing Degree-based Topological Indices for Trees with Given Number of Pendent Vertices + Erratum

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