论文标题
与Euler $ ϕ $函数有关的图
A graph related to Euler $ϕ$ function
论文作者
论文摘要
Euler函数$ ϕ（n）$是小于$ n $的正整数数量，相对较高至$ n $。假设$ ϕ^1（n）= ϕ（n）$和$ ϕ^i（n）= ϕ（ϕ^{i-1}（n））$。令$ a \ subseteq \ mathbb {n} $，$ a_ϕ = \ {ϕ^k（n）| n \在a，k \ in \ mathbb {n} \ cup \ {0 \} \}中。 r，s \ in v，ϕ（r）= s \} $。我们说，如果存在一组自然数量$ a $，则图$ h $是$ g_ϕ $ -graph，以便$ h = g_ϕ（a）$。在本文中，我们研究了图$ g_ϕ（a）$，并研究了一些特定的图形和一些化学树，为$ g_ϕ $ -graph。
Euler function $ϕ(n)$ is the number of positive integers less than $n$ and relatively prime to $n$. Suppose that $ϕ^1(n)=ϕ(n)$ and $ϕ^i(n)=ϕ(ϕ^{i-1}(n))$. Let $A\subseteq \mathbb{N}$, and $A_ϕ=\{ ϕ^k(n)| n\in A , k\in \mathbb{N} \cup \{0\}\}.$ We consider a graph $G_ϕ(A)=(V,E)$, where $V=A_ϕ$ and $E=\{\{r,s\}| r,s\in V, ϕ(r)=s \}$. We say a graph $H$ is a $G_ϕ$-graph, if there exists a set of natural numbers $A$, such that $H=G_ϕ(A)$. In this paper we study the graph $G_ϕ(A)$ and investigate some specific graphs and some chemical trees as $G_ϕ$-graph.
