%0 Journal Article
%T On the anti-forcing number of graph powers
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Soltani, Neda
%A Alikhani, Saeid
%D 2024
%\ 09/01/2024
%V 9
%N 3
%P 497-507
%! On the anti-forcing number of graph powers
%K perfect matching
%K anti-forcing number
%K power of a graph
%R 10.22049/cco.2023.27874.1378
%X 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.
%U http://comb-opt.azaruniv.ac.ir/article_14549_8063c1509ea34ba75de39f928295198a.pdf