Question: Shortest self returning walk

Given a graph G and a vertex v find the shortest self returning walk from that visits all vertices starts at v and comes back to v.

In the below graph the shortest self returning walk which visits all vertices and comes back to first to started vertex

A function which takes a graph G  and  vertex v as input and returns the length of the  shortest self returning walk of that vertex in the below example 10

I am sorry for the error i just saw the change after reading more in deep

For the vertex 7 the shortest self returning walk from that visits all vertices starts at 7 and comes back to 7 It is a walk so edges can repeat

The closed walk which passes through all vertices minimum from vertex 7 is so length 10. is what it means

so it returns 10.