@user36212 I see, thank you for explicitly giving the reduction! This does indeed show hardness for $v > t$.

@user36212 I think you're doing the reduction in the wrong direction. And the "NP-hard" type question here would be to find a maximum size subgraph without an induced copy of $G$. For $t=2$, this turns out to be equivalent to the Max 2-SAT problem, but the condition for $G$ to be avoided is easy to state.

@DouglasZare You are right, I meant upper bounds. Isomorphic graphs obviously have the same reliability polynomial, and there are non-isomorphic graph cases that have the same one also. So there are fewer reliability polynomials than the # of non-isomorphic graph classes (obviously on a fixed number of vertices/edges).

@IgorRivin asymptotics would help but I was wondering if explicit formulas/values were known for certain graph classes. I haven't found any for specifically non-isomorphic connected spanning graphs, only for a subset of these.