Wiener Index and Remoteness in Triangulations and Quadrangulations

Let $G$ be a connected graph. The Wiener index of graph is the sum distances between all unordered pairs vertices. We provide asymptotic formulae for maximum simple triangulations and quadrangulations with given connectivity, as order increases, make conjectures extremal based on computational evidence. If $\overline{\sigma}(v)$ denotes arithmetic mean from $v$ to other vertices $G$, then remoteness defined largest value over $G$. give sharp upper bounds connectivity.