Minimum Wiener Index of Triangulations and Quadrangulations
Combinatorics
2021-12-23 v3
Abstract
The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. We provide formulae for the minimum Wiener index of simple triangulations and quadrangulations with connectivity at least , and provide the extremal structures, which attain those values. Our main tool is setting upper bounds for the maximum degree in highly connected triangulations and quadrangulations.
Cite
@article{arxiv.2003.03873,
title = {Minimum Wiener Index of Triangulations and Quadrangulations},
author = {Éva Czabarka and Trevor Olsen and Stephen Smith and László A. Székely},
journal= {arXiv preprint arXiv:2003.03873},
year = {2021}
}