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 not divisible by three, we show there exists an infinite family of fullerene graphs with the same HOMO-LUMO gap of size . Finally, we discuss how to realize those families in three dimensional space.
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}
}