## Wiener Index in Triangulations and Quadrangulations

- March 6, 2020
- 2:30 p.m.

## Abstract

Let G be a connected graph. The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. We provide upper and lower bounds for the Wiener index of simple triangulations and quadrangulations with given connectivity, and provide the extremal structures which attain these values. Additionally, we provide upper bounds for the maximum degree of highly connected triangulations and quadrangulations.