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Communications in Algebra Volume 35, 2007 - Issue 12
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Original Articles

The Zero-Divisor Graphs Which Are Uniquely Determined By Neighborhoods

Dancheng Lu Department of Mathematics, Suzhou University, Suzhou, ChinaCorrespondence[email protected]
&
Tongsuo Wu Department of Mathematics, Shanghai Jiaotong University, Shanghai, China
Pages 3855-3864 | Received 07 Jun 2006, Published online: 13 Dec 2007

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Read on this site (6)

John D. LaGrange. (2023) Eigenvalues of zero-divisor graphs, Catalan numbers, and a decomposition of eigenspaces. Linear and Multilinear Algebra 0:0, pages 1-12.
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A-Ming Liu & Tongsuo Wu. (2018) Boolean graphs are Cohen–Macaulay. Communications in Algebra 46:10, pages 4498-4510.
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Candace F. Kimball & John D. LaGrange. (2018) The idempotent-divisor graphs of a commutative ring. Communications in Algebra 46:9, pages 3899-3912.
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Meng Ye, Tongsuo Wu, Qiong Liu & Houyi Yu. (2014) Implements of Graph Blow-Up in Co-Maximal Ideal Graphs. Communications in Algebra 42:6, pages 2476-2483.
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Tongsuo Wu, Houyi Yu & Dancheng Lu. (2012) The Structure of Finite Local Principal Ideal Rings. Communications in Algebra 40:12, pages 4727-4738.
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Qiong Liu & Tongsuo Wu. (2009) The Structure of Finite c-Local Rings. Communications in Algebra 37:9, pages 3321-3336.
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Articles from other publishers (17)

John D. LaGrange. (2022) Order-couniversality of the complete infinitary tree: An application of zero-divisor graphs. Journal of Pure and Applied Algebra 226:11, pages 107114.
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D. Scott Dillery & John D. LaGrange. (2019) Spectra of Boolean Graphs Over Finite Fields of Characteristic Two. Canadian Mathematical Bulletin 63:1, pages 58-65.
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David F. Anderson & Ayman Badawi. 2017. Groups, Modules, and Model Theory - Surveys and Recent Developments. Groups, Modules, and Model Theory - Surveys and Recent Developments 23 39 .
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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Meng Ye, Tongsuo Wu, Qiong Liu & Jin Guo. (2014) Graph properties of co-maximal ideal graphs of commutative rings. Journal of Algebra and Its Applications 14:03, pages 1550027.
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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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John D. LaGrange. (2012) Boolean rings and reciprocal eigenvalue properties. Linear Algebra and its Applications 436:7, pages 1863-1871.
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John D. LaGrange. (2018) Characterizations of Three Classes of Zero-Divisor Graphs. Canadian Mathematical Bulletin 55:1, pages 127-137.
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Qiong Liu & Tongsuo Wu. (2012) On Zero-divisor Graphs Whose Cores Contain no Rectangles. Algebra Colloquium 18:04, pages 675-684.
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LI CHEN & TONGSUO WU. (2012) ON RINGS R WHOSE GRAPHS Γ(R) SATISFY CONDITION (K p ) . Journal of Algebra and Its Applications 10:04, pages 665-674.
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S. VISWESWARAN. (2012) SOME RESULTS ON THE COMPLEMENT OF THE ZERO-DIVISOR GRAPH OF A COMMUTATIVE RING. Journal of Algebra and Its Applications 10:03, pages 573-595.
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Qiong Liu & Tong Suo Wu. (2011) Commutative rings whose zero-divisor graph is a proper refinement of a star graph. Acta Mathematica Sinica, English Series 27:6, pages 1221-1232.
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David F. Anderson, Michael C. Axtell & Joe A. SticklesJr.Jr.. 2011. Commutative Algebra. Commutative Algebra 23 45 .
John D. LaGrange. (2010) Weakly central-vertex complete graphs with applications to commutative rings. Journal of Pure and Applied Algebra 214:7, pages 1121-1130.
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Tongsuo Wu & Li Chen. (2012) Simple Graphs and Zero-divisor Semigroups. Algebra Colloquium 16:02, pages 211-218.
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Tongsuo Wu, Qiong Liu & Li Chen. (2009) Zero-divisor semigroups and refinements of a star graph. Discrete Mathematics 309:8, pages 2510-2518.
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Dancheng Lu & Tongsuo Wu. (2009) On bipartite zero-divisor graphs. Discrete Mathematics 309:4, pages 755-762.
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