LAUSR

Abstract Halaš and Jukl associated the zero-divisor graph G to a poset (X,≤) with zero by declaring two distinct elements x and y of X to be adjacent if and only if there is no non-zero lower bound for {x, y}. We characterize all the graphs that can be realized as the zero-divisor graph of a poset. Using this, we classify posets whose zero-divisor graphs are the same. In particular we show that if V is an n-element set, then there exist ∑log2⁡(n+1)≤k≤nnk2k−k−1n−k $\begin{array}{} \sum\limits_{\log_2(n+1)\leq k\leq n}^{}\binom{n}{k}\binom{2^k-k-1}{n-k} \end{array} $ reduced zero-divisor graphs whose vertex sets are V.