On totient graph of a set of positive integers

Abstract

In this paper, we introduce a new class of graphs called totient graph of the set of the first n positive integers. A totient graph, denoted by T(In), is a simple, undirected graph with vertex set In = {1,2,...,n} and any two distinct vertices x and y are adjacent if and only if x + y ∈ P(In), where P(In) = {x ∈ In : x ≡6 0(modφ(n))}.