  The tensor product of two graphs, $G$ and $H$, has a vertex set $V(G)\times
V(H)$ and an edge between $(u,v)$ and $(u',v')$ iff both $u u' \in E(G)$ and $v
v' \in E(H)$. Let $A(G)$ denote the limit of the independence ratios of tensor
powers of $G$, $\lim \alpha(G^n)/|V(G^n)|$. This parameter was introduced by
Brown, Nowakowski and Rall, who showed that $A(G)$ is lower bounded by the
vertex expansion ratio of independent sets of $G$. In this note we study the
relation between these parameters further, and ask whether they are in fact
equal. We present several families of graphs where equality holds, and discuss
the effect the above question has on various open problems related to tensor
graph products.
