Let $G$ be a Petersen graph and $S\subset V(G)$,
how can I compute $e(G[S])$ for non-trivial $S$?
Here $G[S]$ is the induced subgraph of $G$ and $e(G[S])$ is the number of edges of $G[S]$. I think this should be a function of $|S|$, i.e., the size of $|S|$. For specified $S$, say, the five vertices in a 5-cycle, one can come up with $ e(G[S])=|S|=5.\quad[\text{EDITED}] $ But I have no idea how to approach this problem for general $S$.
[EDITED:] Can I bound $e(G[S])$ by a function of $|S|$?