Ali Fawad, Rather Bilal Ahmad, Din Anwarud, Saeed Tareq, Ullah Asad
Institute of Numerical Sciences, Kohat University of Science & Technology, Kohat 26000, Pakistan.
Mathematical Sciences Department, College of Science, United Arab Emirates University, Al Ain P.O. Box 15551, United Arab Emirates.
Entropy (Basel). 2022 Jan 29;24(2):213. doi: 10.3390/e24020213.
Suppose G is a finite group. The power graph represented by P(G) of G is a graph, whose node set is G, and two different elements are adjacent if and only if one is an integral power of the other. The Hosoya polynomial contains much information regarding graph invariants depending on the distance. In this article, we discuss the Hosoya characteristics (the Hosoya polynomial and its reciprocal) of the power graph related to an algebraic structure formed by the symmetries of regular molecular gones. As a consequence, we determined the Hosoya index of the power graphs of the dihedral and the generalized groups. This information is useful in determining the renowned chemical descriptors depending on the distance. The total number of matchings in a graph Γ is known as the -index or Hosoya index. The -index is a well-known type of topological index, which is popular in combinatorial chemistry and can be used to deal with a variety of chemical characteristics in molecular structures.
假设(G)是一个有限群。由(G)的幂图(P(G))所表示的图是这样一个图，其节点集为(G)，并且当且仅当其中一个元素是另一个元素的整数次幂时，两个不同元素相邻。 Hosoya多项式包含许多关于依赖于距离的图不变量的信息。在本文中，我们讨论与由正多边形的对称性形成的代数结构相关的幂图的Hosoya特征（Hosoya多项式及其倒数）。结果，我们确定了二面体群和广义群的幂图的Hosoya指数。此信息对于根据距离确定著名的化学描述符很有用。图(\Gamma)中的匹配总数称为(Z)-指数或Hosoya指数。(Z)-指数是一种著名的拓扑指数，在组合化学中很流行，可用于处理分子结构中的各种化学特征。
