Edge Irregularity Strength of Rooted Product of Certain Families of Graphs

Abstract

Graph theory is one of the most powerful tool in the field of mathematics. Different mathe- maticians work in this field and consider it as a powerful tool in different directions because in recent times graph theory has confirmed as a paramount mathematical tool in various subjects. Now it has emerged as an important mathematical discipline in its own right. There are several types of labelings in graph theory. In this thesis we intend to find the irregular labeling of double graph, rooted product as well as the some family of the Teoplitz graphs. we have divided this thesis into seven chapters. First chapter is about the introduction as well as basic definitions of different types of graphs. In this chapter we have discussed some graph operations along with their examples. In chapter second we have clarified different types of labeling which was defined by well known scholars. At the end of this chapter we have written some known results of edge irregularity strength for certain families of graph. In chapter three we have discussed results related to edge irregularity strength of double graph of path and cycle. we have also proved these results. we believe that these results are accurate. In chapter four we have developed some results for edge irregularity strength of rooted product of cycle and path graphs. In chapter five we find edge irregular labeling of different families of Teoplitz graphs and calculated the edge irregularity strength of Teoplitz graphs.