… Abstract: We compute the number of symmetric r-colorings and the number of
equivalence classes of symmetric r-colorings of the quaternion group. Keywords: quaternion;
symmetric coloring; optimal partition; Möbius function … Identifying Zn with the vertices of a
regular n-gon we obtain that a coloring is symmetric if it is invariant with respect to some
mirror symmetry with an axis crossing the center of the polygon and one of its vertices. …