ISRO 2024

Question

Maximum number of Simple graphs possible with $n$ vertices

1. $2^{n(n-1)/2}$
2. $2^{(n-1)/2}$
3. $2^{n(n+1)/2}$
4. $2^{n(n+1)}$

Answer 1

Let us consider that we have  |E|  edges then total number of the simple graph possible are $2^{|E|}$

So maximum number of edges in the simple are  n(n-1)/2  where “n” are number of vertices

 

So maximum number of simple graphs are $2^{n(n-1)/2}$

so option A is correct