Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 9 3 2024 09 01 On the anti-forcing number of graph powers 497 507 14549 10.22049/cco.2023.27874.1378 EN Neda Soltani Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran Saeid Alikhani Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran Journal Article 2022 06 09 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. https://comb-opt.azaruniv.ac.ir/article_14549_8063c1509ea34ba75de39f928295198a.pdf