It has degree 4, with 20 vertices and 40 edges.
It has girth 4, diameter 4 and radius 3.
Its symmetry group has 3840 elements.
It is bipartite.
It is Hamiltonian.
It is semi-symmetric.
Its distance-list is 1,4,9,6.
The smallest semi-symmetric but not symmetric graph
https://en.wikipedia.org/wiki/Folkman_graph
For copyright details of Wikipedia images see Folkman_Lombardi.svg Folkman_graph_alt.svg.