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Original Articles

Zero-Divisor Graphs of Matrices Over Commutative Rings

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Pages 1186-1192 | Received 20 Aug 2007, Published online: 28 Mar 2009

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Alen Đurić, Sara Jevđenić & Nik Stopar. (2021) Compressed zero-divisor graphs of matrix rings over finite fields. Linear and Multilinear Algebra 69:11, pages 2012-2039.
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Abdul Jalil M. Khalaf, Hina Dilawer, Farkhanda Afzal, Ayesha Maqbool, Deeba Afzal & Faryal Chaudhry. (2020) Right zero divisor graph of 2×2 matrices over Z3. Journal of Information and Optimization Sciences 41:8, pages 1803-1810.
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Shikun Ou & Dein Wong. (2019) Automorphism group of rank-decreasing graph of matrices. Communications in Algebra 47:8, pages 3181-3189.
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Dengyin Wang, Xiaobin Ma & Fenglei Tian. (2016) Automorphism Group of the Rank-decreasing Graph Over the Semigroup of Upper Triangular Matrices. Communications in Algebra 44:9, pages 4088-4096.
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Xiaobin Ma & Dein Wong. (2016) Automorphism group of an ideal-relation graph over a matrix ring. Linear and Multilinear Algebra 64:2, pages 309-320.
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LeahM. Birch, JeremyJ. Thibodeaux & RalphP. Tucci. (2014) Zero Divisor Graphs of Finite Direct Products of Finite Rings. Communications in Algebra 42:9, pages 3852-3860.
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Aihua Li & RalphP. Tucci. (2013) Zero Divisor Graphs of Upper Triangular Matrix Rings. Communications in Algebra 41:12, pages 4622-4636.
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Necla Kırcalı Gürsoy. (2023) Graphs of Wajsberg Algebras via Complement Annihilating. Symmetry 15:1, pages 121.
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A. E. Guterman & S. A. Zhilina. (2023) Cayley–Dickson Split-Algebras: Doubly Alternative Zero Divisors and Relation Graphs. Journal of Mathematical Sciences 269:3, pages 331-355.
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Emil Ilić-Georgijević. (2022) On Homogeneous Co-maximal Graphs of Groupoid-Graded Rings. Bulletin of the Malaysian Mathematical Sciences Society 45:6, pages 3367-3384.
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M. Sivagami & T. Tamizh Chelvam. (2021) Hamiltonian trace graph of matrices. Discrete Mathematics, Algorithms and Applications 14:05.
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Bijon Biswas, S. Kar & M. K. Sen. (2021) Square element graph of square-subtract rings. Discrete Mathematics, Algorithms and Applications 14:04.
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Xinlei Wang, Dein Wong & Fenglei Tian. (2020) Automorphism group of the one-divisor graph over the semigroup of upper triangular matrices. Journal of Algebra and Its Applications 20:11.
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Arif Gursoy, Necla Kircali Gursoy, Tahsin Oner & Ibrahim Senturk. (2021) An alternative construction of graphs by associating with algorithmic approach on MV-algebras. Soft Computing 25:21, pages 13201-13212.
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Aihua Li, Ryan Miller & Ralph P. Tucci. 2020. Advances in Mathematical Sciences. Advances in Mathematical Sciences 173 179 .
A. E. Guterman & S. A. Zhilina. (2019) Relationship Graphs of Real Cayley–Dickson Algebras. Journal of Mathematical Sciences 240:6, pages 733-753.
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F. A. A. Almahdi, K. Louartiti & M. Tamekkante. (2018) The trace graph of the matrix ring over a finite commutative ring. Acta Mathematica Hungarica 156:1, pages 132-144.
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Hengbin Zhang, Jizhu Nan & Gaohua Tang. (2017) Automorphisms of the zero-divisor graph of 2 × 2 matrix ring over ℤps. Journal of Algebra and Its Applications 16:12, pages 1750227.
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José María Grau, Celino Miguel & Antonio M. Oller-Marcén. (2016) On the Zero Divisor Graphs of the Ring of Lipschitz Integers Modulo n. Advances in Applied Clifford Algebras 27:2, pages 1191-1202.
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Anagha Khiste & Vinayak Joshi. (2016) Zero-divisor graphs of matrices over lattices. Discrete Mathematics, Algorithms and Applications 08:04, pages 1650060.
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Raibatak Sen Gupta & M.K. Sen. (2016) Some new results on the graph Γ1(R) over a ring R. Electronic Notes in Discrete Mathematics 53, pages 3-14.
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Long Wang. (2016) Automorphisms of the zero-divisor graph of the ring of all matrices over a finite field . Discrete Mathematics 339:8, pages 2036-2041.
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Long Wang. (2015) A note on automorphisms of the zero-divisor graph of upper triangular matrices. Linear Algebra and its Applications 465, pages 214-220.
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Dein Wong, Xiaobin Ma & Jinming Zhou. (2014) The group of automorphisms of a zero-divisor graph based on rank one upper triangular matrices. Linear Algebra and its Applications 460, pages 242-258.
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C. Miguel. (2013) Balanced zero-divisor graphs of matrix rings. Lobachevskii Journal of Mathematics 34:2, pages 137-141.
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DAVID DOLŽAN & POLONA OBLAK. (2012) THE ZERO-DIVISOR GRAPHS OF RINGS AND SEMIRINGS. International Journal of Algebra and Computation 22:04, pages 1250033.
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Zoran Pucanovic & Zoran Petrovic. (2011) On the radius and the relation between the total graph of a commutative ring and its extensions. Publications de l'Institut Mathematique Publications de l'Institut Math?matique (Belgrade) 89:103, pages 1-9.
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