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Original Articles

Local Rings with Genus Two Zero Divisor Graph

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Pages 2965-2980 | Received 17 Nov 2008, Published online: 18 Aug 2010

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (5)

Xuanlong Ma, Gary L. Walls & Kaishun Wang. (2019) Power graphs of (non)orientable genus two. Communications in Algebra 47:1, pages 276-288.
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K. Selvakumar & M. Subajini. (2018) Commutative rings with genus two annihilator graphs. Communications in Algebra 46:1, pages 28-37.
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K. Selvakumar & V. Ramanathan. (2017) Classification of nonlocal rings with genus one 3-zero-divisor hypergraphs. Communications in Algebra 45:1, pages 275-284.
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Nathan Bloomfield. (2013) The Zero Divisor Graphs of Commutative Local Rings of Order p 4 and p 5 . Communications in Algebra 41:2, pages 765-775.
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T. Tamizh Chelvam & T. Asir. (2013) On the Genus of the Total Graph of a Commutative Ring. Communications in Algebra 41:1, pages 142-153.
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Articles from other publishers (25)

K. Selvakumar & N. Anusha. (2023) On the ideal-based zero-divisor graph of commutative rings. Discrete Mathematics, Algorithms and Applications 16:01.
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Thangaraj Asir, Karuppiah Mano & Turki Alsuraiheed. (2023) Classification of Genus Three Zero-Divisor Graphs. Symmetry 15:12, pages 2167.
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G. Kalaimurugan, P. Vignesh & T. Tamizh Chelvam. (2022) Genus two nilpotent graphs of finite commutative rings. Journal of Algebra and Its Applications 22:06.
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K. Selvakumar, V. Ramanathan & C. Selvaraj. (2022) On the genus of dot product graph of a commutative ring. Indian Journal of Pure and Applied Mathematics 54:2, pages 558-567.
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A. A. Afanas’ev & A. S. Monastyreva. (2023) Compressed and Partially Compressed Zero-Divisor Graphs of Finite Associative Rings. Siberian Mathematical Journal 64:2, pages 291-299.
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Alen Đurić, Sara Jevđenić & Nik Stopar. (2020) Categorial properties of compressed zero-divisor graphs of finite commutative rings. Journal of Algebra and Its Applications 20:05, pages 2150069.
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T. Asir, K. Mano & M. Subathra. 2021. Rings, Monoids and Module Theory. Rings, Monoids and Module Theory 261 285 .
X. Ma & H. Su. (2020) Finite groups whose noncyclic graphs have positive genus. Acta Mathematica Hungarica 162:2, pages 618-632.
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G. Kalaimurugan, P. Vignesh & T. Tamizh Chelvam. (2020) Toroidal zero-divisor graphs of decomposable commutative rings without identity. Boletín de la Sociedad Matemática Mexicana 26:3, pages 807-829.
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A. S. Monastyreva. (2020) Finite Non-Nilpotent Rings with Complete Compressed Zero-Divisor Graphs. Lobachevskii Journal of Mathematics 41:9, pages 1666-1671.
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Gaohua Tang, Guangke Lin & Yansheng Wu. (2019) Associate class graph of zero-divisors of a commutative ring. Journal of Algebra and Its Applications 19:08, pages 2050155.
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T. Tamizh Chelvam & K. Prabha Ananthi. (2019) The genus of graphs associated with vector spaces. Journal of Algebra and Its Applications 19:05, pages 2050086.
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E. V. Zhuravlev & A. S. Monastyreva. (2020) Compressed Zero-Divisor Graphs of Finite Associative Rings. Siberian Mathematical Journal 61:1, pages 76-84.
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T. Asir & K. Mano. (2019) Classification of non-local rings with genus two zero-divisor graphs. Soft Computing 24:1, pages 237-245.
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T. Asir & K. Mano. (2019) Classification of rings with crosscap two class of graphs. Discrete Applied Mathematics 265, pages 13-21.
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T. Asir. (2018) The genus two class of graphs arising from rings. Journal of Algebra and Its Applications 17:10, pages 1850193.
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Huadong Su & Yiqiang Zhou. (2018) Finite commutative rings whose unitary Cayley graphs have positive genus. Journal of Commutative Algebra 10:2.
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K. Selvakumar & V. Ramanathan. (2016) Classification of non-local rings with projective 3-zero-divisor hypergraph. Ricerche di Matematica 66:2, pages 457-468.
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Krishnan Selvakumar & Manoharan Subajini. (2016) Classification of rings with toroidal Jacobson graph. Czechoslovak Mathematical Journal 66:2, pages 307-316.
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David F. Anderson & John D. LaGrange. (2016) Some remarks on the compressed zero-divisor graph. Journal of Algebra 447, pages 297-321.
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Huadong Su, Kenta Noguchi & Yiqiang Zhou. (2014) Finite commutative rings with higher genus unit graphs. Journal of Algebra and Its Applications 14:01, pages 1550002.
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ZORAN S. PUCANOVIĆ, MARKO RADOVANOVIĆ & ALEKSANDRA LJ. ERIĆ. (2014) ON THE GENUS OF THE INTERSECTION GRAPH OF IDEALS OF A COMMUTATIVE RING. Journal of Algebra and Its Applications 13:05, pages 1350155.
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Huadong Su & Pailing Li. (2014) On the Genus of the Zero-Divisor Graph of . International Journal of Combinatorics 2014, pages 1-5.
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Zoran S. Pucanović & Zoran Z. Petrović. (2013) Toroidality of Intersection Graphs of Ideals of Commutative Rings. Graphs and Combinatorics 30:3, pages 707-716.
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David F. Anderson & John D. LaGrange. (2012) Commutative Boolean monoids, reduced rings, and the compressed zero-divisor graph. Journal of Pure and Applied Algebra 216:7, pages 1626-1636.
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