# The Conjugacy Class and Conjugacy Class Graph of Crystallographic Point Groups of Order 12 and Above

### Abstract

In chemistry, crystallographic point group is a set of algebraic groups that maintains at least one point in a fixed position while placing certain restrictions on the rotational symmetries. In this research, the application of group theory and graph theory to the symmetry study of a molecule is presented where the conjugacy classes and conjugacy class graphs of crystallographic point groups of order 12 and above are determined. Conjugacy class is a way of classifying the elements of a group such that two elements *a* and *b* are conjugate if there exists an element *x* and given that *xax*^{-1}=*b*. The conjugacy classes obtained are then used to determine the conjugacy class graph in which their vertex set is the set of non-central classes of a group, that is the vertices are connected if the greatest common divisor of the cardinalities of the corresponding vertices is more than one

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**Mathematical Sciences and Informatics Journal**, [S.l.], v. 2, n. 1, p. 1-8, may 2021. ISSN 2735-0703. Available at: <https://myjms.mohe.gov.my/index.php/mij/article/view/12973>. Date accessed: 16 apr. 2024. doi: https://doi.org/10.24191/mij.v2i1.12973.