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  • 1 Department of Mathematics, University of Neyshabur, P.O.Box 91136-899, Neyshabur, Iran
  • 2 Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran
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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}={0}, where, for a subset S of P, S is the set of all elements xP with xs for all sS. We study some basic properties of G(P). Also, we completely investigate the planarity of G(P).

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