An av-subgraph of graph G$G$ is a subgraph that includes all of the vertices of G$G$. Proving that the number of av-subgraphs of a complete graph with N$N$ vertices which is 2**(N(N+1)/2)$2^{N(N+1)/2}$ is harder than proving the number of av-subgraphs of a graph G with E$E$ edges is 2**E$2^E$.
