On Derivative Euler Phi Function Set-Graphs

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