多边形链图中的完美匹配数(英文)

On the Number of Perfect Matchings in Polygonal Chains

多边形链图的完美匹配数 (即多边形碳氢链状聚合物的 Kekule结构数 )是数学化学研究的重要内容之一 .我们给出了一个求该数的简洁算法 ,并证明该数是一个多项式 .做为应用 ,对于一类特殊的多边形链图 ,给出了具体的表达式 .

The linear fusions of hydrocarbons composed of polygonal rings is an important class of the fusions of hydrocarbons. In terms of graphic theory, such class can be represented as the ‘so called’ polygonal chains. An algorithm to count the number of perfect matchings in polygonal chains (i.e. Kekule structures in fusions) is obtained, which is very easy to calculate by hands (so by computers as well). As an application of this algorithm, we show that the number of perfect matchings in polygonal chains is a polynomial. A formula to count the perfect matchings in a class of polygonal chains is also derived.