@article {
author = {Kala, R. and Kavitha, S.},
title = {A typical graph structure of a ring},
journal = {Transactions on Combinatorics},
volume = {4},
number = {2},
pages = {37-44},
year = {2015},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2015.6177},
abstract = {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 $\Gamma_N^*(R)$.},
keywords = {local ring,nilpotent,planar,Artinian ring},
url = {https://toc.ui.ac.ir/article_6177.html},
eprint = {https://toc.ui.ac.ir/article_6177_95c66f3ddffbab1d427f14e4b0d0e823.pdf}
}