论文标题
在零距离图上，环$ \ mathbb {f} _p+u \ mathbb {f} _p+u^2 \ mathbb {f} _p $
On Zero-Divisor Graph of the ring $\mathbb{F}_p+u\mathbb{F}_p+u^2 \mathbb{F}_p$
论文作者
论文摘要
在本文中，我们讨论了具有身份$ \ mathbb {f} _p+u \ u \ mathbb {f} _p+u^2 \ mathbb {f} _p $ u^3 = 0 $ p $的零分数图。我们发现与环相关的零径向图的集团数，色数，顶点连接，边缘连接性，直径和周长。我们找到了一些拓扑指数和代码的主要参数，这些代码是从零分离器图$γ（r）的发射矩阵得出的。$另外，我们发现邻接和laplacian矩阵的特征值，能量和频谱半径$γ（r）。$ $。
In this article, we discussed the zero-divisor graph of a commutative ring with identity $\mathbb{F}_p+u\mathbb{F}_p+u^2 \mathbb{F}_p$ where $u^3=0$ and $p$ is an odd prime. We find the clique number, chromatic number, vertex connectivity, edge connectivity, diameter and girth of a zero-divisor graph associated with the ring. We find some of topological indices and the main parameters of the code derived from the incidence matrix of the zero-divisor graph $Γ(R).$ Also, we find the eigenvalues, energy and spectral radius of both adjacency and Laplacian matrices of $Γ(R).$
