Abstract
Let \({\mathcal {S}}\) be a commutative ring with \(Z({\mathcal {S}})\) its set of zero-divisors. The extended zero-divisor graph of \({\mathcal {S}}\), denoted by \(\Gamma '({\mathcal {S}})\), is an undirected graph with vertex set \(Z^*({\mathcal {S}})\) and two distinct vertices \(\delta\) and \(\omega\) are adjacent if and only if \(\delta {\mathcal {S}} \cap Ann(\omega ) \ne 0\) or \(\omega {\mathcal {S}} \cap Ann(\delta ) \ne 0\). In this paper, we first characterize finite commutative rings whose extended zero-divisor graph is isomorphic to some well-known graphs and then we classify finite commutative rings whose extended zero-divisor graph is planar, toroidal or projective.
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The authors are deeply grateful to the referee for careful reading of the paper and helpful suggestions.
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Rehman, N., Nazim, M. & Selvakumar, K. On the genus of extended zero-divisor graph of commutative rings. Rend. Circ. Mat. Palermo, II. Ser 72, 3541–3550 (2023). https://doi.org/10.1007/s12215-022-00843-7
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DOI: https://doi.org/10.1007/s12215-022-00843-7