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- Title
The Cayley Graphs of Crystallographic Point Groups Under Hexagonal Crystal System.
- Authors
bin Ab Hamid, Mohd Halimi
- Abstract
In chemistry, point groups are used to describe the molecular symmetries of a molecule. Meanwhile, a crystallographic point group is a set of point group that holds at least one point in a fixed position and have some restriction on the rotational symmetries. In this research, the application of graph theory and group theory on the symmetry study of molecules is presented in which the Cayley graph of crystallographic point groups under the hexagonal crystal system is determined. The generators are also computed for groups C3h, C6, C6h, D3h, C6v, D6and D6h then used to determine the Cayley graph, which is a directed graph representing the group in terms of the generating sets. This research shows that isomorphic crystallographic point groups produce a similar structure to the Cayley graph but different in labelling.
- Subjects
HEXAGONAL crystal system; CAYLEY graphs; POINT set theory; GRAPH theory; GRAPH labelings; GROUP theory
- Publication
ESTEEM, 2021, Vol 17, p77
- ISSN
1675-7939
- Publication type
Article