On correlation of hyperbolic volumes of fullerenes with their properties

TL;DR

This paper explores the relationship between the hyperbolic volumes of fullerene-derived polyhedra and their chemical properties, proposing hyperbolic volume as a new descriptor correlated with known topological indices.

Contribution

It introduces the concept of hyperbolic volume for fullerenes and demonstrates its correlation with chemical indices, offering a novel approach for chemical property prediction.

Findings

Hyperbolic volume correlates with topological indices like Wiener index.

Conjectures on volumes of hyperbolic polyhedra are supported by initial data.

Hyperbolic volume can serve as a chemical descriptor.

Abstract

We observe that fullerene graphs are one-skeletons of polyhedra, which can be realized with all dihedral angles equal to $\pi/2$ in a hyperbolic 3-dimensional space. One of the most important invariants of such a polyhedron is its volume. We are referring this volume as a hyperbolic volume of a fullerene. It is known that some topological indices of graphs of chemical compounds serve as strong descriptors and correlate with chemical properties. We demonstrate that hyperbolic volume of fullerenes correlates with few important topological indices and so, hyperbolic volume can serve as a chemical descriptor too. The correlation between hyperbolic volume of fullerene and its Wiener index suggested few conjectures on volumes of hyperbolic polyhedra. These conjectures are confirmed for the initial list of fullerenes.