当前位置: X-MOL 学术J. Algebra Appl. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Spectrum of the zero-divisor graph of von Neumann regular rings
Journal of Algebra and Its Applications ( IF 0.8 ) Pub Date : 2021-07-15 , DOI: 10.1142/s0219498822501936
Avinash Patil 1 , Kiran Shinde 2
Affiliation  

The zero-divisor graph Γ(R) of a commutative ring R is the graph whose vertices are the nonzero zero divisors in R and two vertices x and y are adjacent if and only if xy=0. We study the adjacency and Laplacian eigenvalues of the zero-divisor graph Γ(R) of a finite commutative von Neumann regular ring R. We prove that Γ(R) is a generalized join of its induced subgraphs. Among the |Z(R)| eigenvalues (respectively, Laplacian eigenvalues) of Γ(R), exactly |B(R)|2 are the eigenvalues of a matrix obtained from the adjacency (respectively, Laplacian) matrix of Γ(B(R))-the zero-divisor graph of nontrivial idempotents in R. We also determine the degree of each vertex in Γ(R), hence the number of edges.



中文翻译:

冯诺依曼正则环的零除数图谱

零除数图Γ(R)交换环的R是其顶点是非零零除数的图R和两个顶点X是的相邻当且仅当X是的=0. 我们研究了零除数图的邻接和拉普拉斯特征值Γ(R)有限交换冯诺依曼正则环的R. 我们证明Γ(R)是其诱导子图的广义连接。之间|Z(R)*|的特征值(分别为拉普拉斯特征值)Γ(R), 确切地|(R)|-2是从邻接(分别为拉普拉斯)矩阵获得的矩阵的特征值Γ((R))- 非平凡幂等的零除数图R. 我们还确定了每个顶点的度数Γ(R),因此是边数。

更新日期:2021-07-15
down
wechat
bug