一类多边形随机链的Edge-Wiener指数

Note on the Edge-Wiener Indices of a Class of Random Polygonal Chains

Edge-Wiener指数是一种新的反映物质物理化学性质的拓扑不变量,它与著名的Wiener指数有着紧密的联系。为了能比较全面地研究一类重要的多边形链的相关性质,结合差分方程和概率论领域一些方法,给出了此类多边形随机链Edge-Wiener指数的期望的具体表达式。作为应用,找到了一类取Edge-Wiener指数极值的多联苯链并重新得到了一些现已发表的结果。最后,研究了Edge-Wiener指数的渐近行为。

Edge-Wiener index is a new topological invariant which is used in the study of physicochemi-cal properties of chemical compounds and is closely associated with the Wiener index. To investigate the related properties of a class of important polygon chains comprehensively,an explicit expression for the expected value of the Edge-Wiener indices of a class of random polygonal chains is given.For applica-tions,the Polyphenyl chains which can achieve the maximum and minimum of the Edge-Wiener indices is found.And some results that have been published in recent papers are revealed.Finally the asymptotic behaviour of Edge-Wiener indices is also considered.