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Permanents of power graphs. (English)
Congr. Numerantium 159, 63-67 (2002).
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 $G$.