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Symmetry 2009, 1(2), 145-152; doi:10.3390/sym1020145

On the Symmetry of a Zig-Zag and an Armchair Polyhex Carbon Nanotorus

1 and 2,*
1 Department of Physics & Young Researchers Club, Islamic Azad University, Kashan, I. R. Iran 2 Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan, I. R. Iran
* Author to whom correspondence should be addressed.
Received: 17 July 2009 / Revised: 13 September 2009 / Accepted: 14 September 2009 / Published: 8 October 2009
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
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A Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. The aim of this paper is to compute the automorphism group of the Euclidean graph of a carbon nanotorus. We prove that this group is a semidirect product of a dihedral group by a group of order 2.
Keywords: Euclidean graph; symmetry; Polyhex carbon nanotorus Euclidean graph; symmetry; Polyhex carbon nanotorus
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Yavari, M.; Ashrafi, A.R. On the Symmetry of a Zig-Zag and an Armchair Polyhex Carbon Nanotorus. Symmetry 2009, 1, 145-152.

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