Abstract
We associate a graph G ∗(P) to a partially ordered set (poset, briefly) with the least element 0, as an undirected graph with vertex set P ∗=P∖{0} and, for two distinct vertices x and y, x is adjacent to y in G ∗(P) if and only if {x,y}ℓ={0}, where, for a subset S of P, S ℓ is the set of all elements x∈P with x≦s for all s∈S. We study some basic properties of G ∗(P). Also, we completely investigate the planarity of G ∗(P).
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Afkhami, M., Barati, Z. & Khashyarmanesh, K. Planar zero divisor graphs of partially ordered sets. Acta Math Hung 137, 27–35 (2012). https://doi.org/10.1007/s10474-012-0231-6
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DOI: https://doi.org/10.1007/s10474-012-0231-6