prove that for every connected graph G, if G has no cycles then for every pair of vertices a,b in G, there is only one path from a to b in G.
the contrapositive of this would be easier to prove but i'm not exactly sure how to do that..
Well what is a cycle?
Is every path from a to b also a path from b to a?
What happens if there are two paths from a to b?
a cycle is a circuit with the only repeated nodes at the beginning and end.
every path from a to b is also a path from b to a
if there are two paths from a to b, then...there is more than one cycle?