Classification of non-local rings with genus two zero-divisor graphs

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Abstract

The zero-divisor graph of a commutative ring R is a simple graph whose vertices are the nonzero zero divisors of R and two distinct vertices are adjacent if their product is zero. In this article, we determine precisely all non-local commutative rings whose zero-divisor graphs have genus two.

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Acknowledgements

The research of T. Asir was in part supported by a Grant from The Science and Engineering Research Board (SERB–MATRICS Project—Ref. MTR/2017/000830). The research of K. Mano was in part supported by a fellowship from The University Grants Commission (Rajiv Gandhi National Fellowship—F1-17.1/2014-15/RGNF-2014-15-SC-TAM-85000).

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Asir, T., Mano, K. Classification of non-local rings with genus two zero-divisor graphs. Soft Comput 24, 237–245 (2020). https://doi.org/10.1007/s00500-019-04345-0

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Keywords

  • Non-local rings
  • Zero-divisor graphs
  • Genus of a graph
  • Double torus