On the Intersection Graphs Associeted to Posets

Let (P, ≤) be a poset with the least element 0. The intersection graph of ideals of P, denoted by G(P), is a graph whose vertices are all nontrivial ideals of P and two distinct vertices I and J are adjacent if and only if I ∩ J ≠ {0}. In this paper, we study the planarity and outerplanarity of the intersection graph G(P). Also, we determine all posets with split intersection graphs.