prove that a connected graph with $n$ vertices has at least $n-1$ edges Show that every connected graph with $n$ vertices has at least $n − 1$ edges.
How can I prove this?  Conceptually, I understand that the following graph has 3 vertices, and two edges:
a-----b-----c
with $a$, $b$ and $c$ being vertices, and $\{a,b\}$, $\{b,c\}$ being edges.
Is there some way to prove this logically?
--UPDATE--
Does this look correct?  Any advice on how to improve this proof would be appreciated.  Thank you.


Consider any arbitrary vertex of the n vertices, call it vertex A. Since the graph is connected, there always exists atleast one simple path(without cycles) from vertex A to all vertices (excluding A). Now for consider two simple paths from A to B and A to C. If B is not same as C, there must be atleast one edge which is different in the two paths. Since atleast n-1(since n-1 vertices excluding A are present) paths exist, n-1 edges are must
