关于富勒烯图的反强迫数
On the anti-forcing number of fullerene graphs
摘要：
一个连通图的反强迫数$G$是使删除这些边后得到的图具有唯一完美匹配的最小边数。本文证明了每个富勒烯的反强迫数至少为4。我们给出了构造所有反强迫数达到下界4的富勒烯的方法。进一步证明了对于每个偶数$n\geq20$（$n\neq22,26$），存在一个反强迫数为4的$n$顶点富勒烯，以及一个反强迫数为5的26顶点富勒烯.
英文摘要：
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 $n\geq20$ ($n\neq22,26$), there exists a fullerene with $n$ vertices that has the anti-forcing number four, and the fullerene with 26 vertices has the anti-forcing number five.
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