There definitely are traceable graphs (hamiltonian-path graph) that have equal number of vertexes and have equal degree information - for example, graph A has vertex A that has degree of three, vertex B degree of four, C degree of three and graph B has vertex A' that has degree of three, vertex B' degree of four, C' degree of three and so forth.
So, what would be the number of distinct traceable graphs that would be like as above?
Or the bound of the number would also be fine.