On Connection Based Topological Descriptors of Magnesium Silicide

Abstract

Chemical graph theory focuses on the physical features of molecular structures using topo- logical descriptors, where topological descriptors are mathematical formulas that repre- sents a molecular structure and can be applied to any graph. Chemical graph theory depend extensively on topological descriptors, particularly in relation with chemical features of molecules. According to the structural characteristics of the graphs implemented in their computation, they can be categorised. This thesis focuses on several types of topologi- cal descriptors for Magnesium Silicide’s molecular structure. The structure denoted by (Mg2Si), comprises of eight Magnesium Mg and four Silicon Si atoms. The structure and shape of the molecular graph are commonly described by the topological indices. The significance of these indices in simulating the chemical characteristics of the Magnesium Silicide’s network is emphasised in the thesis. Chapter 1 of the thesis includes the introduction, which involves the history of graph the- ory, applications, basic definitions and representation of chemical graphs. Chapter 2 includes literature review, some well-known topological descriptors and known results of topological descriptors on different types of graphs. Chapter 3 and 4 includes the construction of chemical structure of Magnesium Silicide, results of degree and connection number-based topological descriptors which are also em- phasized using figures and tables.