If a graph has
2 with 1 degree
1 with 2 degrees
5 with 3 degrees.
If it is not a tree I must prove why.
The only way I can think of to do this is to draw the graph (which I can't replicate here).
When I draw the graph I find I have 2 non-trivial circuits, therefore the graph is not a tree.
Is this the only way to prove the graph is not a tree?