Hello again everyone!

With the Euler's Circuit, do I have to use all vertices and edges?

The question is: find a Euler's circuit in figure 11.44

I counted the degrees and they are all of even numbers. But I can't find my way finding a euler circuit using everything.

But I did this, I just made a subgraph into a euler's circuit.

If a graph has any vertices of odd degree, then it CANNOT have an EULER CIRCUIT.

Euler’s Theorem 1

AND

If a graph is connected and every vertex has even degree, then it has AT LEAST ONE EULER CIRCUIT (usually more). <--- when it says at least one euler circuit, so there are more circuits, but does it use all vertices and edges or not?

Thanks so much!