Prove by induction (and without the use of cycle definition) that if to delete a leaf vertex from a tree graph it will stay as a tree graph.
I think Ive got it wrong but what I did is the following: By the inductive defenition of a tree graph of 'n' vertices, its a graph that been constructed out of a tree of 'n-1' vertices and an attached leaf. But, the same goes for a tree with 'n-1'.
So, can I tell that this is why if we eliminate 1 vertice of a tree graph it will still be a tree graph?