The Topological Study of an Infinite Family of Fullerenes with 10n Carbon Atoms

Abstract

Fullerenes are carbon cage molecules having 12 pentagonal and (n/2 – 10) hexagonal faces, where 20 ≤ n (≠ 22) is an even integer. In this paper, an infinite class of fullerenes with 10n carbon atoms is investigated. We prove that the vertex–PI, Szeged and revised Szeged indices of this family are computed by formulas 150n² − 100n, 250n³ + 3075n − 13800 and 250n³ + 250n² + 4275n − 15650, respectively, when n > 10 is a positive integer. A MATLAB program is also presented that is useful for our calculations.

Keywords:

• Fullerene
• Szeged index
• revised Szeged index
• vertex-PI index

Acknowledgment

We are very grateful to the referees for their corrections and helpful remarks, leading us to improve the paper.