@article {
author = {Soltani, Neda and Alikhani, Saeid},
title = {On the anti-forcing number of graph powers},
journal = {Communications in Combinatorics and Optimization},
volume = {9},
number = {3},
pages = {497-507},
year = {2024},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2023.27874.1378},
abstract = {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.},
keywords = {perfect matching,anti-forcing number,power of a graph},
url = {http://comb-opt.azaruniv.ac.ir/article_14549.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14549_8063c1509ea34ba75de39f928295198a.pdf}
}