Vertex isoperimetric number of a graph - NP-hard? The vertex isoperimetric number of a graph $G=(V,E)$ is
$i_V(G) = \min\{\frac{|N(S)|}{|S|} : S \subseteq V, 1\le |S|\le \frac{|V|}{2}\}$.
Several academic papers state that the problem of computing the vertex isoperimetric number of a graph is NP-hard, without proof or reference.

Can you give a reference where the following problem is shown NP-complete: given a graph $G$ and a number $t$, the question is to decide whether $G$ has vertex isoperimetric number at most $t$?
The following paper:
On an isoperimetric problem for Hamming graphs
L.H. Harper. contains the following:


  The vertex-isoperimetric problem is NP-complete [8] in
  general, so no polynomially bounded solution is known and it is unlikely that one
  exists.


Where reference [8] is
M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, 

This book usually either contains a proof or a reference to the proof.
Unfortunately I have no access to the book at the moment.