Let G be a simple graph with n vertices and m edges. Prove:
If n = 11 and m = 46, show that G is connected.
for the second part of your problem i'll prove a general result:
Claim: suppose a simple graph has vertices and edges. if the graph is not connected, then
Proof. so the graph has a connected component with vertices which is disconnected from the rest of the graph, which has vertices. therefore
it's now easy to see that the inequality is equivalent to which is a true statement because Q.E.D.