I want to know if adding an edge to a undirected acyclic graph introduces no new vertex to the undirected acyclic graph then therefore we can say that adding this edge creates a cycle? I am confident this is correct, but I am looking for a formal proof on this if it is true(preferably a published paper that shows this). My take is that when you add 1 edge to a undirected  we can...Introduce 1 new vertex to the undirected  acyclic graph => we still have a undirectedacyclic graphIntroduce 2 new vertices to the undirected acyclic graph  => we have two connected components that are undirected and acyclic.Introduce 0 new vertex to the undirected acyclic graph => we create a cycle, clearly this adds at least another path to reach the vertices of this edge. 
If adding an edge to an undirected acyclic graph where no new vertex is introduced => cycle?
graphs;graph theory