Symmetry (Oct 2009)

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

  • Morteza Yavari,
  • Ali Reza Ashrafi

DOI
https://doi.org/10.3390/sym1020145
Journal volume & issue
Vol. 1, no. 2
pp. 145 – 152

Abstract

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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.

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