Topic: Graph Theory
Maximum number of Simple graphs possible with n vertices
- A. $2^{n(n-1)/2}$
- B. $2^{(n-1)/2}$
- C. $2^{(n(n+1)/2)}$
- D. $2^{n(n+1)}$
Answer: A. $2^{n(n-1)/2}$
Explanation: In a simple graph with n vertices, the maximum possible number of edges is $n(n-1)/2$. Since each edge can either be present or absent, the total number of simple graphs possible is $2^{n(n-1)/2}$.