This question is inspired by the [Graph Reconstruction Conjecture][1]. Suppose that $\psi$ is some graph invariant and that it is NP-Hard. There is a plethora of examples, of course. Now define $D_{\psi}(G)=\frac{\psi(G)}{\sum_{v \in V(G)}{\psi(G-v)}}$. Let's call this the "deck ratio" of $\psi$.

> Is $D_{\psi}$ NP-Hard?


  [1]: http://en.wikipedia.org/wiki/Reconstruction_conjecture