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 asympto...
