THE ANNIHILATOR GRAPH OF A 0-DISTRIBUTIVE LATTICE

In this article, for a lattice ℒ, we dene and investigate the annihilator graph ag(ℒ) ofl which contains the zero-divisor graph of ℒ as a subgraph. also, for a 0-distributive lattice ℒ, westudy some properties of this graph such as regularity, connectedness, the diameter, the girth and itsdomination number. moreover, for a distributive lattice l with z(ℒ) ≠ {0}, we show that ag(ℒ) = γ(ℒ) if and only if ℒ has exactly two minimal prime ideals. among other things, we consider the annihilatorgraph ag(ℒ) of the lattice ℒ = (d(n);|) containing all positive divisors of a non-prime natural number nand we compute some invariants such as the domination number, the clique number and the chromaticnumber of this graph. also, for this lattice we investigate some special cases in which ag(d(n)) or γ (d(n)) are planar, eulerian or hamiltonian.