Line graphs associated to annihilating-ideal graph attached to lattices of genus one

Let (L,\wedge,\vee) be a lattice with a least element ۰. The annihilating-ideal graph of L, denoted by \mathbb{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 if I\wedge J=\{۰\}. In this paper, we characterize all lattices L whose the graph \mathfrak{L}(\mathbb{AG}(L)) is toroidal.

کلیدواژه ها:

Annihilating-ideal graph ، Genus ، lattice ، line graph ، Toroidal graph