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