University of IsfahanTransactions on Combinatorics2251-86577320180901The annihilator graph of a 0-distributive lattice1182228510.22108/toc.2017.104919.1507ENSaeidBagheriDepartment of Mathematics, Faculty of Mathematical Sciences, Malayer University, Malayer, Iran0000-0002-8394-1337MahtabKoohi KerahroodiDepartment of Mathematics, Faculty of Mathematical Sciences, Malayer University, Malayer, Iran.Journal Article20170629In this article, for a lattice $\mathcal L$, we define and investigate the annihilator graph $\mathfrak {ag} (\mathcal L)$ of $\mathcal L$ which contains the zero-divisor graph of $\mathcal L$ as a subgraph. Also, for a 0-distributive lattice $\mathcal L$, we study some properties of this graph such as regularity, connectedness, the diameter, the girth and its domination number. Moreover, for a distributive lattice $\mathcal L$ with $Z(\mathcal L)\neq\lbrace 0\rbrace$, we show that $\mathfrak {ag} (\mathcal L) = \Gamma(\mathcal L)$ if and only if $\mathcal L$ has exactly two minimal prime ideals. Among other things, we consider the annihilator graph $\mathfrak {ag} (\mathcal L)$ of the lattice $\mathcal L=(\mathcal D(n),|)$ containing all positive divisors of a non-prime natural number $n$ and we compute some invariants such as the domination number, the clique number and the chromatic number of this graph. Also, for this lattice we investigate some special cases in which $\mathfrak {ag} (\mathcal D(n))$ or $\Gamma(\mathcal D(n))$ are planar, Eulerian or Hamiltonian.https://toc.ui.ac.ir/article_22285_719ab505eba5ec2cd4bf741957e5ce29.pdf