@shaktisingh

Generalized solution for this question .....since graph with n nodes can have n(n-1)/2 edges hence total simple graph possible for unlabeled vertices are n(n-1)/2 +1…..(here +1 is because graph with no edges)

example-- for 3 vertices max edges can be 3*2/2=3 hence 4 graphs possible ..(graph with no edge+ graph with 1 edge +graph with 2 edge +graph with 3 edge)

Question is for upto n nodes hence

for upto 1 graph possible only 1

for upto 2 nodes (1+2)

for 3 nodes (1+2+4)

for n nodes (1+2+4+ 7+11+15+….+upto n terms)

nth term of this series =n(n-1)/2 +1

hence for n nodes

**sum of this series =$n(n^{^{2}}+5)$/6… are total simple graphs possible for unlabelled nodes**