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Prove that a connected graph with n vertices has at least $ n-1 $ edges.
Prove by M.I: we know that deg(v) $\ge1$ for all vertices v, since the graph is connected. Then either deg(v)$\ge 2$ for all v, or there exists one vertex with degree 1. How do I actually show this desired result. Any help is appreciated.
Step 1: Let n=1, then there are 1-1=0 edges. True
Step 2: Show that a connected graph with n+1 vertices, it has n+1-1 edges. I need help on this part. Do I need to use the summation of degree (v)= 2 times the number of edges?