University of Guilan Journal of Algebra and Related Topics 2345-3931 9 2 2021 12 01 Poset properties with respect to semi-ideal based zero-divisor graph 111 120 5304 10.22124/jart.2021.19454.1268 EN B Elavarasan Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore - 641 114, India. K Porselvi Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore - 641 114, Tamilnadu, India. Journal Article 2021 04 26 In this paper, we discuss some properties of poset $P$ determined by semi-ideal based zero-divisor graph $G_K(P),$ for a semi-ideal $K$ of $P.$ We investigate some interesting properties if $G_K(P)$ contains a cycle. Further, we prove that if $V(G_K(P))$ is a generalized tree, then $(V(G_K(P))\backslash S_x)\cup K$ and $(V(G_K(P))\backslash S_{\geq x})\cup K$ are prime semi-ideals of $P$. Posets semi-ideals prime semi-ideals cycle and neighborhood https://jart.guilan.ac.ir/article_5304_bcda4b407ce1d80b53f8c29b36bbf837.pdf