Abstract
In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In 1947, Harry Wiener introduced “path number” which is now known as Wiener index and is the oldest topological index related to molecular branching. Hosoya polynomial plays a vital role in determining Wiener index. In this report, we compute the Hosoya polynomials for hourglass and rhombic benzenoid systems and recover Wiener and hyper-Wiener indices from them.
Highlights
Cheminformatics is a new branch of science which relates chemistry, mathematics, and computer sciences
A topological index is a numeric quantity associated with a graph which characterizes the topology of graph and is invariant under graph automorphism [4,5,6,7,8]. ere are numerous applications of graph theory in the field of structural chemistry. e first well-known use of a topological index in chemistry was by Wiener in the study of paraffin boiling points [9]
We study Hosoya polynomials, Wiener index, and hyper-Wiener index of hourglass and rhombic benzenoid systems
Summary
Cheminformatics is a new branch of science which relates chemistry, mathematics, and computer sciences. Ere are numerous applications of graph theory in the field of structural chemistry. E first well-known use of a topological index in chemistry was by Wiener in the study of paraffin boiling points [9]. In order to explain physicochemical properties, various topological indices have been introduced. E Hosoya polynomial of a graph is a generating function about distance distribution, introduced by Haruo Hosoya in 1988 [10]. E Wiener index was first introduced by Harold Wiener in 1947 to study the boiling points of paraffin [9]. It plays an important role in the so-called inverse structure-property relationship problems [15]. We study Hosoya polynomials, Wiener index, and hyper-Wiener index of hourglass and rhombic benzenoid systems
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