On the anti-forcing number of fullerene graphs [article]

Qin Yang, Heping Zhang, Yuqing Lin
2015 arXiv   pre-print
The anti-forcing number of a connected graph G is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching. In this paper, we show that the anti-forcing number of every fullerene has at least four. We give a procedure to construct all fullerenes whose anti-forcing numbers achieve the lower bound four. Furthermore, we show that, for every even n≥20 (n≠22,26), there exists a fullerene with n vertices that has the anti-forcing number
more » ... four, and the fullerene with 26 vertices has the anti-forcing number five.
arXiv:1503.01900v1 fatcat:nhlxp45xuzbalp2jli7goxoa4i