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- Author or Editor: K. Khashyarmanesh x
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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).