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

Symmetry

Morteza Yavari¹ 

[1] ¹Department of Physics & Young Researchers Club, Islamic Azad University, Kashan, I. R. Iran ²Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan, I. R. Iran

关键词: Euclidean graph;    symmetry;    Polyhex carbon nanotorus;   

DOI  :  10.3390/sym1020145

来源: mdpi

【 摘 要 】

A Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [d_ij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix d_ii 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.

【 授权许可】

CC BY   
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.