18
Subgraph of a graph is a graph whose vertex set is a subset of vertex set of the graph and edge set is a subset of the edge set of the graph
1)no vertex,no edge : 1
2)one vertex : 3C1=3
3)two vertices(edge present/not present) : 3C2*2
4)three vertices , no edge : 1
5)3 vertices 1 edge : 3C1=3
6)3 vertices 2 edges : 3C2=3
7)3 vertices 3 edges : 1
Adding these up : 18