论文标题
有限交换环的Cozero偏差图的Wiener索引
Wiener index of the Cozero-divisor graph of a finite commutative ring
论文作者
论文摘要
让$ r $成为团结的戒指。 $γ'（r）$表示的环$ r $的cozero-divisor图是一个无向的简单图形，其顶点是$ r $的所有非零和非单元元素的集合，而两个不同的顶点$ x $和$ $仅在$ x $ x $ x $ x \ notin ry $ $ y $ y y ynon ynos y ynodin ry \ ynnin rx n n.nhy If相邻。在本文中，我们将[24]的一些结果扩展到任意环。在这方面，我们得出了有限的交换环$ r $的Cozero-divisor图的Wiener索引的封闭式公式。作为应用程序，我们计算$γ'（R）$的Wiener索引，当$ r $是整数Modulo $ n $或减少环的产物时。在本文的最后一部分中，我们提供了一个sagemath代码，以计算这些类别的戒指的cozero-divisor图的维也纳索引，包括ring $ \ mathbb {z} _ {n} _ {n} $。
Let $R$ be a ring with unity. The cozero-divisor graph of a ring $R$, denoted by $Γ'(R)$, is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $x \notin Ry$ and $y \notin Rx$. In this article, we extend some of the results of [24] to an arbitrary ring. In this connection, we derive a closed-form formula of the Wiener index of the cozero-divisor graph of a finite commutative ring $R$. As applications, we compute the Wiener index of $Γ'(R)$, when either $R$ is the product of ring of integers modulo $n$ or a reduced ring. At the final part of this paper, we provide a SageMath code to compute the Wiener index of the cozero-divisor graph of these class of rings including the ring $\mathbb{Z}_{n}$ of integers modulo $n$.
