Eccentric Topological Index of the Zero Divisor graph $Γ[\mathbb {Z}_n]$

The characteristic equation and Wiener index of a compressed zero divisor graph

The Zero divisor Graph of a commutative ring $R$, denoted by $Γ[R]$, is a graph whose vertices are non-zero zero divisors of R and two vertices are adjacent if their product is zero. The compressed zero divisor graph $Γ_E[R]$ is the (undirected) graph whose vertices are the equivalence classes such that distinct vertices [r] and [s] are adjacent if and only if rs = 0. In this paper we derive the characteristic polynomial and Wiener index of the Compressed zero divisor graph $Γ_{E}[\mathbb{Z}_m]$ where $m=p^n$ with prime $p$.

环的零因子图的Wiener指数与Wiener复杂度

The Wiener index and the Wiener Complexity of the zero-divisor graph of a ring

本文研究环的零因子图，计算了有限半单环的Wiener指数和有限单环的Wiener复杂度，并给出半单情形下Wiener复杂度的上界。

Wiener index of the Cozero-divisor graph of a finite commutative ring

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 o…

Eigenvalues and Wiener index of the Zero Divisor graph $Γ[\mathbb {Z}_n]$

The Zero divisor Graph of a commutative ring $R$, denoted by $Γ[R]$, is a graph whose vertices are non-zero zero divisors of $R$ and two vertices are adjacent if their product is zero. In this paper, we consider the zero divisor graph $Γ[\mathbb{Z}_n]$ for $n=p^3$ and $n=p^2q$ with $p$ and $q$ primes. We discuss the adjacency matrix and eigenvalues of the zero divisor graph $Γ[\mathbb{Z}_n]$. We also calculate the energy of the graph $Γ[\mathbb{Z}_n]$.

交换环的弱零因子图的Sombor指标与特征值

Sombor index and eigenvalues of weakly zero-divisor graph of commutative rings

本文研究交换环的弱零因子图，确定了整数模环的Sombor指标，并给出其Sombor谱与能量的界。

关于环$ rac{\mathbb{F}_p[u, v]}{\langle u^2,\, v^2, \, uv-vu angle}$零因子图的研究

Graph Theoretic and Spectral Properties of the Zero-Divisor Graph of $\mathbb{F}_p + u\mathbb{F}_p + v\mathbb{F}_p + uv\mathbb{F}_p$

本文研究了一个具有单位元的交换非链环$\mathbb{F}_p + u\mathbb{F}_p + v\mathbb{F}_p + uv\mathbb{F}_p$的零因子图$\Gamma(R)$，确定了其图论性质，包括团数、色数、顶点连通度、边连通度、直径、环长以及拓扑指数，并计算了邻接矩阵、拉普拉斯矩阵和偏心率矩阵的特征值、能量和谱半径。