Minimizing Wiener Index for Vertex-Weighted Trees with Given Weight and Degree Sequences
Combinatorics
2015-09-23 v2
Abstract
In 1997 Klav\v{z}ar 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.
Keywords
Cite
@article{arxiv.1502.01216,
title = {Minimizing Wiener Index for Vertex-Weighted Trees with Given Weight and Degree Sequences},
author = {Mikhail Goubko},
journal= {arXiv preprint arXiv:1502.01216},
year = {2015}
}
Comments
2 figures