It seems that I have given this warning several times today: There are no standard notations.

Usually we say that a graph is Eulerian if it has an Eulerian circuit (all vertices of even degree).

But there are texts that use the term if a graph is simply traceable.

If you have two disjoint graphs of all even vertices then by connecting them with one edge, you have introduced two odd vertices. Therefore the new graph is not Eulerian but it is traceable.