# Thread: Finding the subgraphs of a simple graph.

1. ## Finding the subgraphs of a simple graph.

I've been stumped trying to figure out how to solve this question and I've received conflicting advice. I'm wondering which is correct, and how do actually go about solving this question.

"Let G be a simple graph with m edges and n vertices. How many different subgraphs with n vertices does G have?"

I'm given the following equation for assistance:

If $\displaystyle G = (V, E)$ is a graph (directed or undirected), then $\displaystyle G_1 = (V_1, E_1)$ is called a subgraph of G if $\displaystyle 0 \neq V_1 \subseteq V$ and $\displaystyle E_1 \subseteq E$, where each edge in $\displaystyle E_1$ is incident with vertices in $\displaystyle V_1$

2. ## Re: Finding the subgraphs of a simple graph.

This is a simple combinatorial problem. Each of the $\displaystyle$m$$edges may or may not be included in a subgraph. That gives you \displaystyle 2^m$$ possibilities. (The assumption is that isomorphism is not taken into consideration.)