Independent Functions of Euler Totient Cayley Graph

Graph Theory is the fast growing area of research in Mathematics. The concepts of Number Theory, particularly, the “Theory of Congruence” in Graph Theory, introduced by Nathanson[7], paved the way for the emergence of a new class of graphs, namely, “Arithmetic Graphs”. Cayley graphs are another class of graphs associated with the elements of a group. If this group is associated with some arithmetic function then the Cayley graph becomes an Arithmetic graph. The Cayley graph associated with Euler Totient function is called an Euler Totient Cayley graph and in this paper we study the independent Functions of Euler Totient Cayley graphs. This paper is devoted to the study of independent functions of Euler Totient Cayley Graph in two cases when n is prime and when n is nonprime.