Other name: 3-crown graph
It has degree 2, with 6 vertices and 6 edges.
It has girth 6, diameter 3 and radius 3.
Its symmetry group has 12 elements.
It is bipartite.
It is Hamiltonian.
It is symmetric.
It is 5-arc-transitive.
6-cycle is the skeleton of the hemi-di-dodecagon
6-cycle is the skeleton of the di-hexagon
6-cycle is the skeleton of S2:{6,4} with muliplicity 2
6-cycle is the skeleton of S3:{12,4} with muliplicity 2
6-cycle is the skeleton of N4:{6,4}6 with muliplicity 2
6-cycle is the skeleton of S4:{6,6}3,3 with muliplicity 3
6-cycle is the skeleton of S4:{6,6}3,2 with muliplicity 3