Ace Test Series: Graph Theory - Graph Connectivity

Question

I think the explanation is for edges for which graph is always connected. 

Answer 1

Let a  SIMPLE graph with n nodes .
max no of edges possible are ⁿC2.

if we want to disconnect graph then do one thing just partition original graph in two portion with 1 and n-1 nodes respectively.
now find number of edges in each component.

with 1 node : no edge 
with n-1 nodes : ^n-1C₂ edges.

Total edges are ^n-1C_2..

Comments

The maximum number of edges to be included in G so that graph is not connected

=(n−1)(n−2)/2

=4851