English

Toroidal Fullerenes with the Cayley Graph Structures

Group Theory 2009-02-11 v1 Spectral Theory

Abstract

A central issue in molecular orbital theory is to compute the HOMO-LUMO gap of a molecule, which measures the excitability of the molecule. Thus it would be of interest to learn how to construct a molecule with the prescribed HOMO-LUMO gap. In this paper, we classify all possible structures of fullerene Cayley graphs and compute their spectrum. For any natural number nn not divisible by three, we show there exists an infinite family of fullerene graphs with the same HOMO-LUMO gap of size 2π3n+O(n2)\frac{2\pi}{\sqrt{3}n}+O(n^{-2}). Finally, we discuss how to realize those families in three dimensional space.

Keywords

Cite

@article{arxiv.0902.1706,
  title  = {Toroidal Fullerenes with the Cayley Graph Structures},
  author = {Ming-Hsuan Kang},
  journal= {arXiv preprint arXiv:0902.1706},
  year   = {2009}
}
R2 v1 2026-06-21T12:09:50.924Z