Affiliation:
1. Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R & D Institute of Science and Technology, Chennai, India
2. Department of Mathematics, DRBCCC Hindu College, Chennai, India
Abstract
Molecular structures are characterised by the Hosoya polynomial and Wiener index, ideas from mathematical chemistry and graph theory. The graph representation of a chemical compound that has atoms as vertices and chemical bonds as edges is called a molecular graph, and the Hosoya polynomial is a polynomial related to this graph. As a graph attribute that remains unchanged under graph isomorphism, the Hosoya polynomial is known as a graph invariant. It offers details regarding the quantity of distinct non-empty subgraphs within a specified graph. A topological metric called the Wiener index is employed to measure the branching complexity and size of a molecular graph. For every pair of vertices in a molecular network, the Wiener index is the total of those distances. In this paper, discussed the Hosoya polynomial, Wiener index and Hyper-Wiener index of the Abid-Waheed graphs (AW)a8 and (AW)a10. This graph is similar to Jahangir’s graph. Further, we have extended the research work on the applications of the described graphs.
Reference22 articles.
1. Hosaya Polynomial and Wiener Index of Abid-Waheed Graph ( AW ) p 6;Mahboob;Applied and Computational Mathematics,2022
2. Topological Indices and Their Applications to Circumcised Donut Benzenoid Systems;Arockiaraj;Kekulenes and Drugs, Taylor and Francis Inc,2020
3. Bollobás B. , Modern Graph Theory. By Springer Verlag, New York, xiii+394 pp., softcover. Graduate Texts in Mathematics, 184, 1998.
4. On molecular topological properties of dendrimers;Bokhary;Canadian. J Chem,2016
5. Relationship between the Hosoya polynomial and the hyper-Wiener index;Cash;Applied Mathematics Letters,2002