Summary: Let $G$ be a connected graph, and let $G^r$ be the $r$th power of $G$. We show that the sequence $\text{perm}(G)$, $\text{perm}(G^2),\dots,\text{perm}(G^d)$ is a strictly increasing sequence where $\text{perm}(G^r)$ denotes the permanent of the adjacency matrix of $G^r$ and $d$ is the diameter of $G$.