  Let $G=(V,E)$ be a simple connected graph. A perfect matching (or Kekul\'e
structure in chemical literature) of $G$ is a set of disjoint edges which
covers all vertices of $G$. The anti-forcing number of $G$ is the smallest
number of edges such that the remaining graph obtained by deleting these edges
has a unique perfect matching and is denoted by $af(G)$. For every
$m\in\mathbb{N}$, the $m$th power of $G$, denoted by $G^m$, is a graph with the
same vertex set as $G$ such that two vertices are adjacent in $G^m$ if and only
if their distance is at most $m$ in $G$. In this paper, we study the
anti-forcing number of the powers of some graphs.
