| Autor: |
Ali F; Institute of Numerical Sciences, Kohat University of Science & Technology, Kohat 26000, Pakistan., Rather BA; Mathematical Sciences Department, College of Science, United Arab Emirates University, Al Ain P.O. Box 15551, United Arab Emirates., Din A; Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China., Saeed T; Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia., Ullah A; Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, Pakistan. |
| Abstrakt: |
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 Z -index or Hosoya index. The Z -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. |
