Suppose we formed a simple graph with 8 vertices.

Then it will have one unique adjacency matrix representation.

So, the number of simple graphs with 8 vertices = no. of 8×8 symmetric matrices whose elements are either 0 or 1 except the diagonal elements which are zero always.

Now, a 8×8 matrix has 64 cells. Substracting the diagonal cells we have 56 cells. On the upper half of the matrix has (56/2) = 28 cells

Now, for each of the 28 cells we have 2 options 1 or 0.

So,the number of 8×8 symmetric matrices where the elements are either 0 or 1 except the diagonal elements are 2^28

So,the number of simple graphs with 8 vertices is 2^28.