There is a real problem with definitions here. Textbooks and authors do not always agree on the definition ofEulerian Graphs.

It seems that most current texts agree that an Eulerian graph is one in which there is aclosed walk, no edge can be repeated. In this case show thatall vertices are even.

On the other hand, we can find older texts that talk abouttraceable graphsbeing Eulerian. That is, there is a walk( not necessarily closed) that includes each edge exactly once. In this case,there are at most two odd vertices.

So check your text material for the definition in use.