Suppose that we set the number of vertexes in a graph (and suppose that in a graph, there is no subgraph separate or isolated from other subgraphs).
Then, there are several ways to connect the vertexes using edges.
Out of those graphs possible, there will be some graphs which have hamiltonian paths (I am not talking of cycles) and graphs that do not have hamiltonian paths.
We know that some graphs can be redrawn without changing edge and vertex information into another graph. (e.g. rotation, reflection etc.)
So, if we count the number of total graphs possible that hamiltonian paths, how many of them will be virtually equal to each other? And how do you get the number?
Also, for graphs that do not have hamiltonian paths, how many of them will be virtually equal to each other? How do you get the number?