A typical graph structure of a ring

Transactions on Combinatorics

S. Kavitha¹  R. Kala¹ 

[1] Manonmaniam Sundaranar University;

关键词: local ring;    nilpotent;    planar;    Artinian ring;   

DOI  :  

来源: DOAJ

【 摘 要 】

The zero-divisor graph of a commutative ring R with respect to nilpotent elements is a simple undirected graph $Gamma_N^*(R)$ with vertex set Z_N(R)*, and two vertices x and y are adjacent if and only if xy is nilpotent and xy is nonzero, where Z_N(R)={x in R: xy is nilpotent, for some y in R^*}. In this paper, we investigate the basic properties of $Gamma_N^*(R)$. We discuss when it will be Eulerian and Hamiltonian. We further determine the genus of $Gamma_N^*(R)$.

【 授权许可】

Unknown