Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A graph related to Euler $\phi$ function   Euler function $\phi(n)$ is the number of positive integers less than $n$ and
relatively prime to $n$. Suppose that $\phi^1(n)=\phi(n)$ and
$\phi^i(n)=\phi(\phi^{i-1}(n))$. Let $A\subseteq \mathbb{N}$, and $A_{\phi}=\{
\phi^k(n)| n\in A , k\in \mathbb{N} \cup \{0\}\}.$ We consider a graph
$G_{\phi}(A)=(V,E)$, where $V=A_{\phi}$ and $E=\{\{r,s\}| r,s\in V, \phi(r)=s
\}$. We say a graph $H$ is a $G_\phi$-graph, if there exists a set of natural
numbers $A$, such that $H=G_{\phi}(A)$. In this paper we study the graph
$G_{\phi}(A)$ and investigate some specific graphs and some chemical trees as
$G_\phi$-graph.

9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio