The Wiener index of vertex colorings
Combinatorics
2025-10-27 v3
Abstract
The Wiener index of a vertex coloring of a graph is defined to be the sum of all pairwise geodesic distances between vertices of the same color. We provide characterizations of vertex colorings of paths and cycles whose Wiener index is as large as possible over various natural collections. Along the way we establish a connection between the majorization order on tuples of integers and the Wiener index of vertex colorings on paths and cycles.
Cite
@article{arxiv.2503.18920,
title = {The Wiener index of vertex colorings},
author = {Viktoriya Bardenova and Neal Bushaw and Brent Cody and Paul Fay and Maya Tennant},
journal= {arXiv preprint arXiv:2503.18920},
year = {2025}
}
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