University of Isfahan Transactions on Combinatorics 2251-8657 3 3 2014 09 01 A note on the zero divisor graph of a lattice 51 59 5626 10.22108/toc.2014.5626 EN T. Tamizh Chelvam Manonmaniam Sundaranar University S. Nithya Manonmaniam Sundaranar University Journal Article 2013 09 06 ‎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 $\Gamma(L)$‎. https://toc.ui.ac.ir/article_5626_80f88a878c7d9f2b5f4422c943a90ae7.pdf