Topological Indices of Graphs and Some Related Aspects

Abstract

This project explores the application of graph theory in chemistry, emphasizing topological indices such as the Leap Eccentric Connectivity Index (LECI) and Leap Zagreb Indices. These indices serve as mathematical descriptors to model molecular structures and predict chemical properties, contributing to quantitative structure- property (QSPR) and structure-activity relationships (QSAR). The study includes graph theory concepts, including vertices, edges, and connectivity. Detailed computations of the Leap Eccentric Connectivity Index (LECI) and Leap Zagreb Indices for various types of graphs, including complete, bipartite, wheel, and star graphs. Extensions to specialized graph structures like subdivision graphs, windmill graphs, and flower graphs are also included. This project is divided into five chapters. Chapter 1 provides basic terminologies, definitions and notions from graph theory and Leap Eccentric connectivity indices. Chapter 2 gives a literature review. Chapter 3 is about main results of the project while a discussion is provided in chapter 4. The references used in the project are given in chapter 5.