论文标题
正整数的正确除数图
Proper divisor graph of a positive integer
论文作者
论文摘要
正整数$ n $的适当除数$υ_n$是简单的图形，其顶点是$ n $的适当除数，并且仅当$ n $ divide $ divide $ uv $时，两个不同的顶点$ u，v $在相邻的情况下与之相邻。图$υ_n$在对环$ \ mathbb {z} _n $的零除数图中起重要作用。在本文中，我们研究了$υ_n$的一些图理论属性，并确定图形参数，例如集团数字，色数，色数，色度索引，独立数，匹配数，匹配数，统治号，顶点，顶点和边缘覆盖数$υ_n$。我们还确定了$υ_n$的自动形态组。
The proper divisor graph $Υ_n$ of a positive integer $n$ is the simple graph whose vertices are the proper divisors of $n$, and in which two distinct vertices $u, v$ are adjacent if and only if $n$ divides $uv$. The graph $Υ_n$ plays an important role in the study of the zero divisor graph of the ring $\mathbb{Z}_n$. In this paper, we study some graph theoretic properties of $Υ_n$ and determine the graph parameters such as clique number, chromatic number, chromatic index, independence number, matching number, domination number, vertex and edge covering numbers of $Υ_n$. We also determine the automorphism group of $Υ_n$.
