Zero-divisor graphs in commutative rings

DOI10.1007/978-1-4419-6990-3_2zbMath1225.13002OpenAlexW2224521589MaRDI QIDQ3172051

David F. Anderson, Michael Axtell, Joe Stickles

Publication date: 5 October 2011

Published in: Commutative Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4419-6990-3_2

Mathematics Subject Classification ID

Development of contemporary mathematics (01A65) Ideals and multiplicative ideal theory in commutative rings (13A15) History of commutative algebra (13-03)

Related Items (90)

Planarity and outerplanarity indexes of the zero-divisor graphs ⋮ Projective zero divisor graphs of partially ordered sets ⋮ ON THE ASSOCIATED GRAPHS TO A COMMUTATIVE RING ⋮ Some results on the complement of the comaximal ideal graphs of commutative rings ⋮ On the clique number of the complement of the annihilating ideal graph of a commutative ring ⋮ Cut structures in zero-divisor graphs of commutative rings ⋮ Graph invariants of the line graph of zero divisor graph of \(\mathbb{Z}_n \) ⋮ Unnamed Item ⋮ On the edge metric dimension and Wiener index of the blow up of graphs ⋮ The Wiener index of the zero-divisor graph of \(\mathbb{Z}_n\) ⋮ Universal adjacency spectrum of zero divisor graph on the ring and its complement ⋮ THE DIAMETER OF THE ZERO-DIVISOR GRAPH OF THE IDEALIZATION OF THE RING R IN R ⋮ Graph theoretic representation of rings of continuous functions ⋮ Dot product graphs and domination number ⋮ The subgroup graph of a group ⋮ On two extensions of the classical zero-divisor graph ⋮ A combinatorial development of Fibonacci numbers in graph spectra ⋮ On the Total Graph of a Ring and Its Related Graphs: A Survey ⋮ Classification of non-local rings with projective 3-zero-divisor hypergraph ⋮ On torsion elements and their annihilators ⋮ Hamiltonian trace graph of matrices ⋮ On the signless Laplacian and normalized Laplacian spectrum of the zero divisor graphs ⋮ A generalization of the annihilating ideal graph for modules ⋮ The regular digraph associated to a poset ⋮ On the planarity of a graph associated to a commutative ring and on the planarity of its complement ⋮ Graph of Linear Transformations Over $$\mathbb {R}$$ ⋮ The \(L\)-total graph of an \(L\)-module ⋮ On a spanning subgraph of the annihilating-ideal graph of a commutative ring ⋮ Some remarks on the compressed zero-divisor graph ⋮ On nonzero component graph of vector spaces over finite fields ⋮ Classification of the toroidal Jacobson graphs ⋮ Bideterministic weighted automata ⋮ Boolean rings and reciprocal eigenvalue properties ⋮ Order two element graph over a group ⋮ On the complement of the total zero-divisor graph of a commutative ring ⋮ Zero-divisor super-\(\lambda\) graphs ⋮ Zero-divisor graphs of small upper irredundance number ⋮ Poset graphs and the lattice of graph annihilators ⋮ The automorphism group of nonzero component graph of vector space ⋮ A Note on the Uniqueness of Zero-Divisor Graphs with Loops (Research) ⋮ When is the complement of the zero-divisor graph of a commutative ring planar? ⋮ Survey article: Graphical representations of factorizations in commutative rings ⋮ Toroidal zero-divisor graphs of decomposable commutative rings without identity ⋮ When is the complement of the zero-divisor graph of a commutative ring complemented? ⋮ A study of the generalized outerplanar index of zero-divisor graphs ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Some results on a spanning subgraph of the complement of the annihilating-ideal graph of a commutative reduced ring ⋮ On zero-divisor graphs of commutative rings without identity ⋮ On the genus of the zero-divisor graph of \(\mathbb Z_n\) ⋮ The genus of graphs associated with vector spaces ⋮ On the extended zero divisor graph of commutative rings ⋮ The Zero-Divisor Graph of a Commutative Semigroup: A Survey ⋮ Commutative rings with genus two annihilator graphs ⋮ On defensive alliance in zero-divisor graphs ⋮ Compressed zero-divisor graphs of matrix rings over finite fields ⋮ On the Annihilator Graph of a Commutative Ring ⋮ On Zero-Divisors in Skew Inverse Laurent Series Over NonCommutative Rings ⋮ Some Remarks on the Graph Γ_I(R) ⋮ On the line graph for zero-divisors of \(C(X)\) ⋮ Zero divisor graph of a lattice with respect to an ideal ⋮ Classification of rings with toroidal annihilating-ideal graph ⋮ Commutative Boolean monoids, reduced rings, and the compressed zero-divisor graph ⋮ Unnamed Item ⋮ The nil-graph of ideals of a commutative ring ⋮ Annihilating submodule graph for modules ⋮ When the line graphs of the unit, unitary and total graphs are planar and outerplanar ⋮ Nonzero Component Graph of a Finite Dimensional Vector Space ⋮ Unnamed Item ⋮ Divisor graph of the complement of Γ(R) ⋮ On the complement of a graph associated with the set of all nonzero annihilating ideals of a commutative ring ⋮ Unnamed Item ⋮ Zero-divisor Labelings of Graphs ⋮ Classification of rings with crosscap two class of graphs ⋮ The exact zero-divisor graph of a reduced ring ⋮ The embedding of annihilating-ideal graphs associated to lattices in the projective plane ⋮ Annihilator Ideal-Based Zero-Divisor Graphs Over Multiplication Modules ⋮ Unnamed Item ⋮ Classification of non-local rings with genus two zero-divisor graphs ⋮ The Semilattice of Annihilator Classes in a Reduced Commutative Ring ⋮ On the Dot Product Graph of a Commutative Ring ⋮ ZERO-DIVISOR GRAPHS OF ÖRE EXTENSION RINGS ⋮ Unnamed Item ⋮ On gracefully and harmoniously labeling zero-divisor graphs ⋮ Graphs derived from multirings ⋮ ON THE REGULAR DIGRAPH OF IDEALS OF COMMUTATIVE RINGS ⋮ THE ZERO-DIVISOR GRAPH OF A MODULE ⋮ Annihilators in zero-divisor graphs of semilattices and reduced commutative semigroups

This page was built for publication: Zero-divisor graphs in commutative rings