Cordial and magic type labelings

Abstract

A graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. Labeled graphs are becoming an increasingly useful family of Mathematical Models for a broad range of applications. In this thesis we study cordial type and Magic type labeling and also introduce new types of labeling related to them. A graph with vertex set V is said to have pr ime labeling if there exists a bijection f :V(G)and#8594;{1,2,..., |V|} such that for each edge xy and#949; E(G) , f(x) and f(y) are relatively prime. A Prime cordial labeling of a graph G with vertex set V is a bijection f from V to {1,2, ,|V|} such that if each edge uv is assigned the label 1 if gcd(f(u),f(v))=1 and 0 if gcd(f(u),f(v))gt1, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by atmost 1. The existence of prime and prime cordial labeling for special graph structures derived from the fundamental graphs are studied. The concept of signed product cordial labeling is introduced and exhibited for some fundamental graphs and tree related graphs along with some general results. Graph labeling is studied with a new direction using the relations over a finite set of positive integers. New graph structures are constructed using relations. The concepts of modulo magic labeling and modulo bimagic labeling are introduced. The notion of magic labeling is extended by introducing P3-magic labeling and study for various graphs. Some results on Z3-magic labeling are also been discussed. The finite state automata over the alphabet {0, 1} is interpreted as a directed graph with binary labeling for the edges and analyze the language recognized by the automata. Based on the above notion cordial words and cordial languages are introduced. Some interesting sequences over numbers are obtained using number theory technique over the cordial words recognized by the finite automata. newline newline newline