The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs

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 vertices u,v∈ V(G) is called the distance, d (u,v), between the vertices u,v. 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≥3. The Wiener index is the sum of distances between all pairs of vertices of G as W(G)= ( ) { } ( ) , . ,

Schultz Polynomials and Their Topological Indices of Jahangir Graphs <i>J</i><sub>2,m</sub>

“…[30]- [35] Jahangir graphs J n,m for m ≥ 3, is a graph on nm + 1 vertices i.e., a graph consisting of a cycle C nm with one additional vertex which is adjacent to m vertices of C nm at distance n to each other on C nm . Theorem 1.…”

Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of ℤ ℊ Liu1, Rauf2, Aslam3 et al. 2022Journal of Function Spaces1000View full textAdd to dashboardCite

“…Randic Connectivity index, Zagreb Indices, the Harmonic index, Atom bond Connectivity, and Geometric Arithmetic index are degree-based topological indices. Some well-known distance-based topological indices are the Wiener index, Hosoya index, and Estrada index [20,21]. For details related to the computation of Hosoya and Harary polynomial of zero divisor graphs associated to some commutative rings, the readers can see [22][23][24].…”

Distance-Based Topological Polynomials Associated with Zero-Divisor Graphs

“…Some well-known topological indices based on the degrees of a graph are the Randić connectivity index, Zagreb indices, Harmonic index, atom bond connectivity, and geometric arithmetic index. e Wiener index, Hosaya index, and Estrada index are distance-based topological indices [10,11]. Topological indices formulate the criteria for the development of compound structures, and numerical activities on these structures extend multidisciplinary research.…”