Wiener Index and Remoteness in Triangulations and Quadrangulations

@article{Czabarka2021WienerIA,
  title={Wiener Index and Remoteness in Triangulations and Quadrangulations},
  author={{\'E}va Czabarka and Peter Dankelmann and Trevor Olsen and L{\'a}szl{\'o} A. Sz{\'e}kely},
  journal={Discret. Math. Theor. Comput. Sci.},
  year={2021},
  volume={23}
}
Let $G$ be a a connected graph. The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. We provide asymptotic formulae for the maximum Wiener index of simple triangulations and quadrangulations with given connectivity, as the order increases, and make conjectures for the extremal triangulations and quadrangulations based on computational evidence. If $\overline{\sigma}(v)$ denotes the arithmetic mean of the distances from $v$ to all other… 
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