TY - JOUR

T1 - On correlation of hyperbolic volumes of fullerenes with their properties

AU - Egorov, A. A.

AU - Vesnin, A. Yu

N1 - Funding Information: Authors are thankful to anonymous reviewers for valuable comments. The work was supported in part by the Theoretical Physics and Mathematics Advancement Foundation "BASIS". Publisher Copyright: © 2020 A. A. Egorov et al., published by De Gruyter.

PY - 2020/11/28

Y1 - 2020/11/28

N2 - We observe that fullerene graphs are one-skeletons of polyhedra, which can be realized with all dihedral angles equal to π/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.

AB - We observe that fullerene graphs are one-skeletons of polyhedra, which can be realized with all dihedral angles equal to π/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.

KW - fullerene

KW - graph

KW - hyperbolic geometry

KW - volume

KW - Wiener index

UR - http://www.scopus.com/inward/record.url?scp=85099176608&partnerID=8YFLogxK

U2 - 10.1515/cmb-2020-0108

DO - 10.1515/cmb-2020-0108

M3 - Article

AN - SCOPUS:85099176608

VL - 8

SP - 150

EP - 167

JO - Computational and Mathematical Biophysics

JF - Computational and Mathematical Biophysics

SN - 2544-7297

IS - 1

ER -