On discerning symmetry properties of graphs

Enumeration of a class of IPR hetero-fullerenes

Hetero-fullerenes are fullerenes in which some of the carbon atoms are replaced by other atoms. This paper uses the P?lya theorem to count the number of their possible positional isomers and chiral isomers. To do this, the computer algebra system GAP was applied to compute this number for a class of IPR hetero-fullerenes with Ih point group symmetry. These fullerenes were constructed by means of the leapfrog principle.

Symmetry of tetrahydroxycalix[4]arenes

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, the character table and the automorphism group of the Euclidean graph of tetrahydroxycalix[4]arenes were computed. .

New computer program to calculate the symmetry of molecules

In this paper we, present some MATLAB and GAP programs and use them to find the automorphism group of the Euclidean graph of the C80 fullerence with connectivity and geometry of Ih symmetry point group. It is proved that this group has order 120 and is isomorphic to Ih≊Z2×A5, where Z2 is, a cyclic group of order 2 and A5 is the alternating group on five symbols.

Symmetry properties of tetraammine platinum(II) with C2v and C4v point groups

Let G be a weighted graph with adjacency matrix A=[a(ij)]. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix D=[d(ij)], where for i not = j, d(ij) 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 different nuclei. Balasubramanian (1995) computed the Euclidean graphs and their automorphism groups for benzene, eclipsed and staggered forms of ethane and eclipsed and staggered forms of ferrocene. This paper describes a simple method, by means of which it is possible to calculate the automorphism group of weighted graphs. We apply this method to compute the symmetry of tetraammine platinum(II) with C2v and C4v point groups.