I need to answer to this (apparently) simple question. In my opinion, since a tree has $n-1$ edges, a graph with these characteristics couldn't exist. In fact, whatever $n$ is chosen, I don't know what happens to the other vertices of the graph but I know that two of them have degree $n-1$. This means already having 2(n-1) edges in the graph that is larger than n-1 and therefore can not be a tree (in other words I am forced to define a cycle that in trees are not allowed).
Can it be reasonable to answer the question in this way?