ON THE TOROIDAL ANNIHILATING-IDEAL GRAPHS OF A LATTICE

Let (L; ^;_) be a lattice with a least element 0. The annihilating-ideal graph of L, denoted by AG(L), is a graph whose vertex set is the set of all non-trivial ideals of L and, for every two distinct vertices I and J, the vertex I is adjacent to J if and only ifI ^ J = f0g. In this paper, we study the toroidality of the annihilating-ideal graphs of nite lattices.

Keywords:

Annihilating-ideal graph , Genus , Lattice , Toroidal graph