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