**:** Goubko M.
**:** Minimizing Wiener Index for Vertex-Weighted Trees with Given Weight and Degree Sequences

**:**
** ( ):** Kraguevac University

**:** 2016
** :** ..

** :** MATCH Commun. Math. Comput. Chem.

** () :** V. 75, No 1
** :** M. Goubko, Minimizing Wiener Index for Vertex-Weighted Trees with Given Weight and Degree Sequences, MATCH Commun. Math. Comput. Chem., 2016, V. 75, No 1, P. 3-27

**:** In 1997 Klavzar 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.

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