Abstract
Let G be a simple connected graph having vertex set V and edge set E. The vertex-set and edge-set of G denoted by V(G) and E(G), respectively. The length of the smallest path between two vertices is called the distance. Mathematical chemistry is the area of research engaged in new application of mathematics in chemistry. In mathematics chemistry, we have many topological indices for any molecular graph, that they are invariant on the graph automorphism. In this research paper, we computing the Wiener index and the Hosoya polynomial of the Jahangir graphs $J_5,m$ for all integer number $m \geq 3$.
Highlights
The degree of a vertex vεV(G) is the number of vertices joining to v and denoted by dv Topological indices of a simple graph are numerical descriptors that are derived from graph of chemical compounds
We present some properties of the Wiener index and the Hosoya polynomial and we introduce a closed formula of this and the correspondent polynomial of the Jahangir graphs J5,m for all integer number m≥3
We introduce a method to compute the Wiener index and the Hosoya polynomial of the Jahangir graphs J5,m in continue
Summary
In a series of papers, the Wiener index and the Hosoya polynomial of some molecular graphs and Nanotubes are computed. We present some properties of the Wiener index and the Hosoya polynomial and we introduce a closed formula of this and the correspondent polynomial of the Jahangir graphs J5,m for all integer number m≥3.
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