On Derivative Euler Phi Function Set-Graphs

Abstract

In this paper, we study some graph theoretical properties of two derivative Euler Phi function set-graphs. For the Euler Phi function $\varphi (n)$, $n\in \mathbb{N}$, the set $S_{\varphi }(n)=\{i:\gcd (i,n)=1,1\le i\le n\}$ and the vertex set is $\{v_i:i\in S_{\varphi }(n)\}$. Two graphs $G_d(S_{\varphi }(n))$ and $G_p(S_{\varphi }(n))$, defined with respect to divisibility adjacency and relatively prime adjacency conditions, are studied.

12 Pages, 3 Figures