Poset graphs and the lattice of graph annihilators

DOI10.1016/j.disc.2013.02.004zbMath1261.05041OpenAlexW1990249427MaRDI QIDQ1945949

John D. LaGrange, Kyle A. Roy

Publication date: 17 April 2013

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2013.02.004

zbMATH Keywords

Boolean algebraannihilatorpartially ordered setzero-divisor graph

Mathematics Subject Classification ID

Partial orders, general (06A06) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Lattices (06B99)

Related Items (20)

Order-couniversality of the complete infinitary tree: an application of zero-divisor graphs ⋮ Zero-divisor graphs and total coloring conjecture ⋮ Unnamed Item ⋮ The annihilation graphs of commutator posets and lattices with respect to an ideal ⋮ Chordal and perfect zero-divisor graphs of posets and applications to graphs associated with algebraic structures ⋮ On the metric determination of linear dependence graph ⋮ CORRECTION TO ‘ON THE COMPLEMENT OF THE ZERO-DIVISOR GRAPH OF A PARTIALLY ORDERED SET’ ⋮ On graphs with equal coprime index and clique number ⋮ Metric Properties of Non-Commuting Graph Associated to Two Groups ⋮ ON THE COMPLEMENT OF THE ZERO-DIVISOR GRAPH OF A PARTIALLY ORDERED SET ⋮ Unnamed Item ⋮ The Zero-Divisor Graph of a Commutative Semigroup: A Survey ⋮ The annihilation graphs of commutator posets and lattices with respect to an element ⋮ On the connectedness of the complement of the zero-divisor graph of a poset ⋮ Unnamed Item ⋮ On the spectrum of linear dependence graph of a finite dimensional vector space ⋮ ON WEAKLY PERFECT ANNIHILATING-IDEAL GRAPHS ⋮ Beck's coloring of finite product of commutative ring with unity ⋮ On the line graphs of zero-divisor graphs of posets ⋮ Annihilators in zero-divisor graphs of semilattices and reduced commutative semigroups

Cites Work

• The zerodivisor graph of a qoset
• The zero-divisor graphs of posets and an application to semigroups
• On Beck's coloring of posets
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• The zero-divisor graph of a lattice
• The zero-divisor graph of a commutative semigroup
• Zero-divisor graphs, von Neumann regular rings, and Boolean algebras.
• Zero-divisor graphs in commutative rings
• On Realizing Zero-Divisor Graphs
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