Faculty of Engineering and Natural Sciences, Department of Mathematics, Bursa Technical University, 16320 Bursa, Turkey.
Instituto de Matemáticas, Universidad de Antioquia Medellín, Colombia.
Math Biosci Eng. 2022 Jul 11;19(10):9842-9852. doi: 10.3934/mbe.2022458.
Coronoid systems are natural graph representations of coronoid hydrocarbons associated with benzenoid systems, but they differ in that they contain a hole. The Hosoya index of a graph G is defined as the total number of independent edge sets, that are called k-matchings in G. The Hosoya index is a significant molecular descriptor that has an important position in QSAR and QSPR studies. Therefore, the computation of the Hosoya index of various molecular graphs is needed for making progress on investigations. In this paper, a method based on the transfer matrix technique and the Hosoya vector for computing the Hosoya index of arbitrary primitive coronoid systems is presented. Moreover, the presented method is customized for hollow hexagons by using six parameters. As a result, the Hosoya indices of both each arbitrary primitive coronoid system and also each hollow hexagon can be computed by means of a summation of four selected multiplications consisting of presented transfer matrices and two vectors.
冠状体系是与苯环体系相关的冠状烃的自然图表示，但它们的不同之处在于它们包含一个孔。图 G 的 Hosoya 指数定义为独立边集的总数，在 G 中称为 k-匹配。Hosoya 指数是一个重要的分子描述符，在 QSAR 和 QSPR 研究中具有重要地位。因此，需要计算各种分子图的 Hosoya 指数，以便在研究中取得进展。本文提出了一种基于转移矩阵技术和 Hosoya 向量的方法，用于计算任意原始冠状体系的 Hosoya 指数。此外，该方法通过使用六个参数对空心六边形进行了定制。结果，通过对四个选定的乘法（由提出的转移矩阵和两个向量组成）的求和，可以计算出每个任意原始冠状体系和每个空心六边形的 Hosoya 指数。
