Can a graph with 11 vertices and 56 edges exist?

Question

Can a simple graph with the following property exist?

The graph is to have 11 vertices and 56 edges.

Thanks for the help.

Answer 1

No.

We can have maximum number of edges in a complete graph.

For $n $ vertices complete graph $k_n$ we have $\frac{n(n-1)}{2}$ edges.

For 11 vertices we can have $11\cdot 10 /2 = 55$ edges. Hence it is not possible.