Next Article in Journal
Visual Symmetry. By Magdolna Hargittai and István Hargittai, World Scientific Publishing, 2009; 224 pages. Price: US48 / £ 36 ISBN 978-981-283-531-4
Next Article in Special Issue
Tetraquark Spectroscopy: A Symmetry Analysis
Previous Article in Journal / Special Issue
Supersymmetry of Generalized Linear Schrödinger Equations in (1+1) Dimensions
Article Menu

Article Versions

Export Article

Open AccessArticle
Symmetry 2009, 1(2), 145-152;

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

Department of Physics & Young Researchers Club, Islamic Azad University, Kashan, I. R. Iran
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)
Download PDF [168 KB, uploaded 9 October 2009]


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 (CC BY 3.0).

Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top