It has degree 2, with 9 vertices and 9 edges.
It has girth 9, diameter 4 and radius 4.
Its symmetry group has 18 elements.
It is not bipartite.
It is Hamiltonian.
It is symmetric.
It is 8-arc-transitive.

Regular maps

9-cycle is the skeleton of the di-nonagon
9-cycle is the skeleton of C7:{9,4} with muliplicity 2

Lists of Graphs
Index to Regular Maps