Analysing Some Topological Indices of the Line Graph Derived from the K-subdivision of the Wheel Graph

Abstract

Topological indices play a crucial role in the mathematical characterization of chemical structures and complex networks. In this paper, we analyze several topological indices of the line graph derived from the k-subdivision of the wheel graph Wn. The k-subdivision of a graph is obtained by replacing each edge with a path of k edges, transforming the original structure into a more intricate graph. The line graph of this k-subdivision further encodes adjacency relationships between edges, enabling a deeper structural analysis. Firstly, we focused on degree-based topological indices, namely the Randic index, atom bond connectivity index, geometric arithmetic index, the first and the second Zagreb in dices and co-indices, the first and the second multiple Zagreb indices and co-indices, hyper Zagreb index, forgotten index, augmented Zagreb index, Balaban index, redefined Zagreb type indices for Analysing some topological indices of the line graph derived from the K-subdivision of the Wheel graph . These indices provide insights into the connectivity and complexity of the graph. Additionally, we analyze the behavior of these indices with respect to the parameter k and the number of vertices n in the original wheel graph. Our f indings reveal trends and relationships between k, n, and the computed indices, shedding light on the impact of k-subdivision on graph-theoretic properties. Theresults presented herein contribute to the broader study of graph invariants and their applications in mathematical chemistry, structural biology, and network theory