ACE Test Series

Question

Comments

but it's not a simple means multi-edge is also considered right ??

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Oh yes..I laid more stress on "not connected"..  if answer is C then it would mean they have not framed the question in a proper way.. :/ Else don't know :P

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@Magma , probably they meant in the question that G is not connected graph , and then they are asking to find the maximum number of edges possible, graph will be simple in this case.

Answer 1

C should be answer

if a graph has more than $\frac{(n−1)(n−2)}{2}$ then it is connected.

A simple undirected graph with n vertices can have at most $\frac{n.(n−1)}{2}$edges.

Now disconnect the graph by disconnected one of its vertices(means remove all the edges that are incident on the nth vertex).
The maximum number of edges between the remaining n−1 vertices can be   $\frac{(n−1)(n−2)}{2}$
Now if u add 1 more edge to the graph it will again connect the nth vertex.