"DISTANCE-BASED TOPOLOGICAL ACHARYA POLYNOMIAL AND INDICES OF HAMILTONIAN GRAPHS"

Authors

Shailaja Shirakol, SDMCET, Dharwad, India.

Manjula Kalyanshetti, Jain College of Engineering, Belagavi, India.

Abstract

Let G be a connected graph, and let H(G) denote the Hamiltonian graph of GEvery complete graph with more than two vertices is a Hamiltonian graph. In this paper, a simple graph was transformed into the Hamiltonian graph structure and several topological indices based ondistance for Hamiltonian graphs H [G] were determined. The distance d[G] (xi, xj) between the vertices Vi and Vj of graph G is equal to the shortest path length thatconnect the two vertices. The number of vertex pairs of G, whose distance is l is denoted by d(G, l). The distance–based topological indices based on Acharya Polynomial considered in this study are as follows: Wiener index (W), hyper–Wiener index (WW), Harary index (H), Reciprocal Terminal Wiener index (TW).