graph theory

Question

Counts

There is a graph, how to find a Hamiltonian path in it, or any other mini-route that intersects all vertices, the graph is different, but coplanar (when depicted on a plane, the edges do not intersect, in fact only neighboring vertices are connected), you need to find some kind of route to the minimum number of times to pass through the same vertices.
Z.s. I forgot the most important thing, the algorithm should work from any vertex of the graph

Answer 1

It seems to be the Traveling Salesman Problem

Answer 2

If you need a Hamiltonian cycle (chain), then there is only a search with a return. But “the minimum number of times to pass through the same vertices”, here, probably, we must first try to find a Hamiltonian cycle (chain), and then increase the max. possible number of occurrences of vertices.