Symmetry of benzenoid chains
DOI:
https://doi.org/10.20450/mjcce.2006.275Keywords:
symmetry group, benzenoid chains, Euclidean graphAbstract
Graph theory provides an elegant and natural representation of molecular symmetry and the resulting group expressed in terms of permutations is isomorphic to the permutation-inversion group of Longuet-Higgins. In this paper, using the group theory package GAP, we compute the automorphism group of the Euclidean graph of benzenoid chains.
References
N. Trinajsti_, Chemical Graph Theory, CRC, Boca Raton, FL,1992.
P. R. Bunker, The rotational-torsional wavefunctions of molecules that have two identical co-axial rotors Mol. Phys., 8 (1), 81–91 (1964).
S. L. Altmann, Induced Representation in Crystal & Molecules, Academic Press, London, 1977.
G. S. Ezra, Symmetry Properties of Molecules, Lecture Notes in Chemistry, 28, Springer, 1982.
H. C. Longuet-Higgins, The symmetry groups of nonrigid molecules, Mol. Phys., 6 (5), 445–460 (1963).
P. R. Bunker, Molecular Symmetry in Spectroscopy, Academic Press, 1979.
M. Randi_, Croat. Chem, Acta, 49, 643 (1977).
M. Randi_, On discerning symmetry properties of graphs, Chem. Phys. Letters, 42 (2), 283–287 (1976).
K. Balasubramanian, Graph theoretical perception of molecular symmetry, Chem. Phys. Letters, 232, 415–423 (1995).
K. Balasubramanian, Applications of combinatorics and graph theory to spectroscopy and quantum chemistry, Chem. Rev., 85, 599–618 (1985).
K. Balasubramanian, Studies Phys. Theor. Chem., 23, 149–168 (1983).
K. Balasubramanian, Generating functions for the nuclear spin statistics of nonrigid molecules, J. Chem. Phys., 75, 4572–4585 (1981).
K. Balasubramanian, Nonrigid group theory, tunneling splittings, and nuclear spin statistics of water pentamer: (H2O)5, J. Phys. Chem., 108, 5527–5536 (2004).
K. Balasubramanian, Group theoretical analysis of vibrational modes and rovibronic levels of extended aromatic C48N12 azafullerene, Chem. Phys. Letters, 391, 64–68 (2004).
K. Balasubramanian, Nuclear spin statistics of extended aromatic C48N12 azafullerene, Chem. Phys. Letters, 391, 69–74 (2004).
A. R. Ashrafi, M. Hamadanian, Symmetry Properties of Some Chemical Graphs, Croat. Chem. Acta, 78, 159–163 (2005).
A. R. Ashrafi, On Non-Rigid Group Theory for Some Molecules, MATCH Commun. Math. Comput. Chem., 53 (1), 161–174 (2005).
R. Darafsheh, Y. Farjami, A. R. Ashrafi, Computing the Full Non-Rigid Group of Tetranitrocubane and Octanitrocubane Using Wreath Product, MATCH Commun. Math. Comput. Chem., 54 (1), 53 (2005).
M. Dabirian, A. Iranmanesh, The Full Non-Rigid Group Theory for Trimethylamine-BH3 Complex, MATCH Commun. Math. Comput. Chem., 54 (1), 75–88 (2005).
M. Schonert et al., GAP, Groups, Algorithms and Programming. Lehrstuhl für Mathematik, RWTH, Aachen, 1992.
M. Ghorbani, A. Gholami, Symmetry of Pyrene and Triphenylmethane Molecules, MATCH Commun. Math. Comput. Chem., 55 (1), 65–72 (2006).
S. Fujita, A Proof for the Existence of Five Stereogenicity Types on the Basis of the Existence of Five Types of Subgroups of RS-Stereoisomeric Groups. Hierarchy of Groups for Restructuring Stereochemistry (Part 3), MATCH Commun. Math. Comput. Chem., 54 (1), 39–52 (2005).
S. Fujita, Orbits Among Molecules. A Novel Way of Stereochemistry Through the Concepts of Coset Representations and Sphericities (Part 2), MATCH Commun. Math. Comput. Chem., 55 (1), 5–38 (2006).
V. V. Iliev, The Genetic Reactions of Ethane, MATCH Commun. Math. Comput. Chem. 56 (1), 21–95 (2006).
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