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Projective zero divisor graphs of partially ordered sets

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Abstract

The zero divisor graph of a partially ordered set (poset, briefly) \((P, \le )\) with the least element 0, which is denoted by \(G^*(P)\), is an undirected graph with vertex set \(P^*= P{\setminus } \{0\}\) 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 \(x\in P\) with \(x\le s\), for all \(s\in S\). In this paper we completely characterize all posets P with projective zero divisor graphs \(G^*(P)\).

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Acknowledgments

The authors would like to express her deep gratitude to Prof. Kazem Khashyarmanesh and Dr. Mojgan Afkhami for many valuable comments which have greatly improved the quality of the paper.

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  1. Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran

    A. Parsapour & Kh. Ahmad Javaheri

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  1. A. Parsapour
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  2. Kh. Ahmad Javaheri
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Correspondence to A. Parsapour.

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Parsapour, A., Javaheri, K.A. Projective zero divisor graphs of partially ordered sets. Afr. Mat. 28, 575–593 (2017). https://doi.org/10.1007/s13370-016-0464-6

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