Computing Wiener Index of $C_{12n}$ Fullerenes

Abstract

Since the Wiener index has been successful in the study of benzenoid systems and boiling points of alkanes, it is natural to examine this number for the study of fullerenes, most of whose cycles are hexagons. This topological index is equal to the sum of distances between all pairs of vertices of the respective graph. It was introduced in $1947$ by one of the pioneers of this area, Harold Wiener, who realized that there are correlations between the boiling points of paraffins and the structure of the molecules. The present paper is the first attempt to compute the Wiener index of an infinite class of fullerenes. Further, we obtain a correlation between the values of the Wiener index and the boiling point of such fullerenes for the first time.