The Zero-Divisor Graph of a Commutative Ring

1999/07/01 by David F. Anderson, Philip S. Livingston · 41 citations
Mathematics · #Rings, Modules, and Algebras #Advanced Topics in Algebra #Algebraic structures and combinatorial models

paper · doi:10.1006/jabr.1998.7840

Citations

• Coloring of commutative rings

Cited by

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• Lengths of Paths and Cycles in Zero-Divisor Graphs and Digraphs of Semigroups
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• Genera of zero-divisor graphs with respect to ideals
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• A zero divisor graph determined by equivalence classes of zero divisors
• Betti Numbers of Sequentially Cohen-Macaulay Co-Chordal Graphs and Their Applications
• Cohen-Macauleyness of the Zero-Divisor Graph of a Boolean Poset
• Remarks on the zero-divisor graph of a commutative ring
• A Bipartite Graph Linking Units and Zero-Divisors
• The Homomorphism Submodule Graph
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• Commutative rings with toroidal zero-divisor graphs
• Eigenvalues of zero-divisor graphs of finite commutative rings
• Beck's Conjecture For Multiplicative Lattices
• On the non-zero divisor graph of the Hamilton quaternions over \mathbb Z_2ⁿ
• The Homology Groups of Zero Divisor Graphs of Finite Commutative Rings
• Coloring of graphs associated to zero-divisors
• On the structure and skeletals of principal ideal graphs of inverse semigroups
• On Distribution of Laplacian Eigenvalues of Graphs
• On varieties of rings whose finite rings are determined by their zero-divisor graphs
• Embeddings of the line graphs associated with the essential graphs of commutative rings
• Some results on the ideal-based cozero-divisor graph of a commutative ring
• The n-total graph of a commutative ring
• Zero-Divisor Graphs of ℤ_n, their products and D_n
• On the strong metric dimension of the complement of the zero-divisor graph of a lattice
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• Unity Product Graph of Some Commutative Rings
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• Locating-Dominating Sets and Identifying Codes of a Graph Associated to a Finite Vector Space