@article {
author = {Tamizh Chelvam, T. and Nithya, S.},
title = {A note on the zero divisor graph of a lattice},
journal = {Transactions on Combinatorics},
volume = {3},
number = {3},
pages = {51-59},
year = {2014},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2014.5626},
abstract = {Let $L$ be a lattice with the least element $0$. An element $x\in L$ is a zero divisor if $x\wedge y=0$ for some $y\in L^*=L\setminus \left\{0\right\}$. The set of all zero divisors is denoted by $Z(L)$. We associate a simple graph $\Gamma(L)$ to $L$ with vertex set $Z(L)^*=Z(L)\setminus \left\{0\right\}$, the set of non-zero zero divisors of $L$ and distinct $x,y\in Z(L)^*$ are adjacent if and only if $x\wedge y=0$. In this paper, we obtain certain properties and diameter and girth of the zero divisor graph $\Gamma(L)$. Also we find a dominating set and the domination number of the zero divisor graph $\Gamma(L)$.},
keywords = {zero divisor graph,lattice,atomic lattice,ideal,dominating set},
url = {https://toc.ui.ac.ir/article_5626.html},
eprint = {https://toc.ui.ac.ir/article_5626_80f88a878c7d9f2b5f4422c943a90ae7.pdf}
}