Geodesic
On the Intersection Graphs Associeted to Posets
Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 1, pp. 105-117

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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.
Keywords: poset, intersection graph, split graph, planar graph, outerplanar graph 
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Afkhami, M.; Khashyarmanesh, K.; Shahsavar, F. On the Intersection Graphs Associeted to Posets. Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 1, pp. 105-117. http://geodesic.mathdoc.fr/item/DMGAA_2020_40_1_a8/