Operation with graphs

Question

I´m trying to apply the Euler theorem (V+F=E+2 on plane graphs) for a concrete graph (the following one).

Thing is that I can use to operations: 1) Delete a node of grade 2 (that is, 2 edges on it) 2) Delete a edge

The idea is obtain a graph with 3 nodes (and grade of all them will be 2), so then apply a Lemma that asserts: V + F = E + 2.

Here are my steps:

Please, help me. Maybe I´m wrong, but I think that this is the idea.

Thanks!

Answer 1

Finally I get it.

Thing is that for apply the Lemma its enough to obtain 3 nodes with any of grade at least 1. So this a (probably) solution:

Thanks for the support! :)