Edge Irregularity Strength of Certain Families of Toeplitz Graph

Abstract

There are several types of labeling, in graph theory, such as irregular labeling, magic labeling, anti-magic labeling, and cordial labeling. In this thesis we intend to find the irregular labeling or irregular assignment of some family of the Toeplitz graph. Graph theory is a very powerful tool of pure and applied mathematics. It concerns with different fields of science and has wide applications. This thesis is divided into four chapters. In the very first chapter which is about the introduction we define some of the initial definitions of graph theory such as, vertices, edges, graph, degree of graph, complete graph, walk, path, cycle, subgraph, isomorphic graph, connected graph, bipartite graph, matrix of graph, adjacency matrix, Toeplitz matrix and Toeplitz graph. In second chapter we define different types of labeling such as, vertex labeling, edge labeling, total labeling, irregular labeling, vertex irregular labeling, edge irregular labeling, and the irregularity strength of some families of Toeplitz graph. In this work this aspects is also a key component and will be discussed in detail through this chapter. In third chapter of this dissertation, we find vertex irregular labeling and edge irregular labeling. Finally we finds the edge irregularity strength of the following families of Toeplitz � �𝑛 〈4,8〉,𝑇𝑛 〈5,10〉 𝑎𝑛𝑑 𝑇𝑛 〈6,12〉. graph such that � �𝑛 〈3,6〉, In the last chapter, we conclude our thesis and used suitable references. Though there are the other research scholars who have made research papers on this topic, yet this work is unique in its significance and scope because no one has worked on it.