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A typical graph structure of a ring | ||
| Transactions on Combinatorics | ||
| مقاله 4، دوره 4، شماره 2، شهریور 2015، صفحه 37-44 اصل مقاله (259.25 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2015.6177 | ||
| نویسندگان | ||
| R. Kala* ؛ S. Kavitha | ||
| Manonmaniam Sundaranar University | ||
| چکیده | ||
| 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 $\mathcal{Z}_N(R)^*$, and two vertices $x$ and $y$ are adjacent if and only if $xy$ is nilpotent and $xy\neq 0$, where $\mathcal{Z}_N(R)=\{x\in R: xy~\text{is nilpotent, for some} y\in R^*\}$. 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 $\Gamma_N^*(R)$. | ||
| کلیدواژهها | ||
| local ring؛ nilpotent؛ planar؛ Artinian ring | ||
| مراجع | ||
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