The equivalence class [r] of an element r\in \mathsf{R} is the set of zero-divisors s such that ann(r)=ann(s), that is, [r]= \{s\in \mathsf{R} : ann(r)=ann(s). The compressed zero-divisor graph, denoted by \Gamma_c(\mathsf{R}), is the compression of a zero-divisor graph, in which the vertex set is the set of all equivalence classes of nonzero zero-divisors of a ring \mathsf{R}, that is, the vertex set of \Gamma_c(\mathsf{R}) is \mathsf{R}_e -\{[0], [1]\}, where \mathsf{R}_e =\{[r] : r\in \mathsf{R}\} and two distinct equivalence classes [r] and [s] are adjacent if and only if rs = 0. In this article, we investigate the planarity of \Gamma_c(\mathsf{R}) for some finite local rings of order p^2, p^3 and determine the planarity of compressed zero-divisor graph of some local rings of order 32, whose zero-divisor graph is nonplanar. Further, we determine values of m and n for which \Gamma_c(\mathbb{Z}_n) and \Gamma_c(\mathbb{Z}_n[x]/(x^m)) are planar.






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   Alghamdi, Ahmad M., Bhat, M. Imran, Pirzada, S.