The following is a valid Euler path in the graph of counties in central Maryland.
Counties in Central Maryland
Carroll
Foderick
Howard
Baltimore
Montgomery
1. Carroll to Baltimore
2. Baltimore to Howard
3. Howard to Frederick
4. Frederick to Montgomery
No, because, by the Theorem, this graph cannot contain an Euler path.
No, because some edges are used twice.
Yes, this is a valid Euler path.
No, because you do not start and stop in the same place.
No, because not every edge is used exactly once.