  A coprime labeling of a graph of order $n$ is an assignment of distinct
positive integer labels in which adjacent vertices have relatively prime
labels. Restricting labels to only the set $1$ to $n$ results in a prime
labeling. In this paper, we consider families of graphs in which a prime
labeling cannot exist with the goal being to minimize the largest value of the
labeling set, resulting in a minimum coprime labeling. In particular, prism
graphs, generalized Petersen graphs with $k=2$, and stacked prism graphs are
investigated for minimum coprime labelings.
