On the Wiener (r,s)-complexity of fullerene graphs: Fullerenes, Nanotubes and Carbon Nanostructures: Vol 0, No 0

Summary

Fullerene graphs are mathematical fashions of fullerene molecules. The Wiener (r,s)-complexity of a fullerene graph G with vertex set V(G) is the variety of pairwise distinct values of (r,s)-transmission $t{r}_{r,s}(v)$ of its vertices v: $t{r}_{r,s}(v)=\sum _{u\in V(G)}{\sum }_{i=r}^{s}d{(v,u)}^i$ for optimistic integer r and s. The Wiener (1,1)-complexity is called the Wiener complexity of a graph. Irregular graphs have most complexity equal to the variety of vertices. No irregular fullerene graphs are recognized for the Wiener complexity. Fullerene (IPR fullerene) graphs with n vertices having the maximal Wiener (r,s)-complexity are counted for all $n\le 100$ ($n\le 136$) and small r and s. The irregular fullerene graphs are additionally introduced.