Draw a graph that is :

no self$-$loops and has neither an Eulerian path nor an Eulerian circuit

and No vertex has degree $1$

and it is impossible to remove an edge to make a graph with an Eulerian circuit or an Eulerian path, but it is possible to add an edge to produce a graph with an Eulerian circuit or an Eulerian path.

Could you please explain how you did that? I want to understand the process.