Fullerenes with the maximum Clar number
Combinatorics
2014-11-03 v2
Abstract
The Clar number of a fullerene is the maximum number of independent resonant hexagons in the fullerene. It is known that the Clar number of a fullerene with n vertices is bounded above by [n/6]-2. We find that there are no fullerenes whose order n is congruent to 2 modulo 6 attaining this bound. In other words, the Clar number for a fullerene whose order n is congruent to 2 modulo 6 is bounded above by [n/6]-3. Moreover, we show that two experimentally produced fullerenes C80:1 (D5d) and C80:2 (D2) attain this bound. Finally, we present a graph-theoretical characterization for fullerenes, whose order n is congruent to 2 (respectively, 4) modulo 6, achieving the maximum Clar number [n/6]-3 (respectively, [n/6]-2).
Cite
@article{arxiv.1410.7030,
title = {Fullerenes with the maximum Clar number},
author = {Yang Gao and Qiuli Li and Heping Zhang},
journal= {arXiv preprint arXiv:1410.7030},
year = {2014}
}