A graph and its unique subgraphs. Any graph G with edges contains at least two unique subgraphs: G itself and the graph obtained by deleting all edges of G. The complete graphs on more than one vertex have just two unique subgraphs.

How do you find the number of subgraphs?

In order to see this, note that a subgraph is the set of the edges included. Each edge is either in the subgraph or it isn't. This means that the number of subgraphs of a graph is equal to 2NumOfEdges. In the complete bipartite graph Kr,s, the number of edges is rs, so the number of subgraphs of Kr,s is 2rs.

How do I find all the subgraphs on a graph?

If the graph is disconnected then start another DFS from any vertex which is still not visited after the first round of DFS and check again if all the vertices are visited. Repeat the above process until all the vertices are visited. Keep counting the no of DFS calls. This will be our answer to the number of subgraphs.