报告方式：腾讯会议 ID：905 127 519 会议密码：210119
邀请人：许宝刚教授
摘要：In 1985 Randi\'{c} and Klein proposed the {\em innate degree of freedom} of a Kekul\'e structure, i.e. the least number of double bonds can determine this entire Kekule structure, nowadays it is called the forcing number of a perfect matching by Harary. Recently, the anti-forcing number of a single perfect matching of a graph was also proposed. Let $G$ be a graph with a perfect matching $M$. The smallest number of edges of $E(G)\backslash M$ whose deletion maintains a unique perfect matching $M$ is the {\em anti-forcing number} of $M$. The maximum anti-forcing number of perfect matchings of a graph play an important role in theoretical chemistry. For example, it was shown that the maximum anti-forcing numbers of perfect matchings of a hexagonal system and (4,6)-fullerene graphs are equal to their Fries numbers respectively. In this talk we present a mini-max result, two upper bounds on maximum anti-forcing numbers and the corresponding extremal graphs, and a relation with the global forcing number.