# 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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