The Cyclic Graph of a Finite Group

Table 1

Cyclic graph	Isomorphic graph	Vertex degree sequences	Clique number	Geodetic number	Planarity
Γ𝑍2×𝑍2	𝐾1,3	3, 1, 1, 1	2	3	Planar
Γ𝑆3		5, 2, 2, 1, 1, 1	3	5	Planar
Γ𝑍2×𝑍2×𝑍2	𝐾1,7	7, 1, 1, 1, 1, 1, 1, 1	2	7	Planar
Γ𝑍2×𝑍4		7, 5, 3, 3, 3, 3, 1, 1	4	6	Planar
Γ𝐷8		7, 3, 3, 3, 1, 1, 1, 1	4	7	Planar
Γ𝑄8		7, 7, 3, 3, 3, 3, 3, 3	4	6	Planar
Γ𝑍3×𝑍3		8, 2, 2, 2, 2, 2, 2, 2, 2	3	8	Planar
Γ𝐷10		9, 4, 4, 4, 4, 1, 1, 1, 1, 1	5	9	Nonplanar
Γ𝑍2×𝑍6		11, 9, 9, 5, 5, 5, 3, 3, 3, 3, 1, 1	6	10	Nonplanar
Γ𝐷12		11, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1	6	11	Nonplanar
Γ𝑄4×3		11, 11, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3	6	10	Nonplanar
Γ𝐴4		11, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1	3	11	Planar
Γ𝐷14		13, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1	7	13	Nonplanar