Zero-divisor semigroups and refinements of a star graph.

DOI10.1016/J.DISC.2008.06.008zbMath1188.20073OpenAlexW1973078259MaRDI QIDQ1025512

Li Chen, Qiong Liu, Tong Suo Wu

Publication date: 19 June 2009

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

Full work available at URL: https://doi.org/10.1016/j.disc.2008.06.008

zbMATH Keywords

counting formulasnilpotent semigroupsrefinements of star graphs

Mathematics Subject Classification ID

Applications of graph theory (05C90) General structure theory for semigroups (20M10) Commutative semigroups (20M14) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (19)

On the inclusion ideal graph of a ring. ⋮ Some properties of the idempotent graph of a ring ⋮ On the Unit Graph of a Non-commutative Ring ⋮ Planar zero divisor graphs of partially ordered sets ⋮ Minimal prime ideals and cycles in annihilating-ideal graphs ⋮ Annihilator graphs of a commutative semigroup whose zero-divisor graphs are a complete graph with an end vertex ⋮ On some graphs associated to commutative semirings ⋮ The Zero-Divisor Graph of a Commutative Semigroup: A Survey ⋮ The Classification of the Annihilating-Ideal Graphs of Commutative Rings ⋮ The Annihilating-Ideal Graph of a Commutative Ring with Respect to an Ideal ⋮ Zero-divisor graphs of partially ordered sets ⋮ Zero divisor graph of a lattice with respect to an ideal ⋮ The annihilation graphs of commutator posets and lattices with respect to an element ⋮ ON THE IDEMPOTENT GRAPH OF A RING ⋮ Unnamed Item ⋮ On Zero-divisor Graphs Whose Cores Contain no Rectangles ⋮ The Structure of Finitec-Local Rings ⋮ The Inclusion Ideal Graph of Rings ⋮ A note on subspace sum graph of vector spaces

Cites Work

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• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• When a zero-divisor graph is planar or a complete \(r\)-partite graph
• Zero divisor graphs of semigroups.
• The zero-divisor graph of a commutative semigroup
• Zero-divisor graphs, von Neumann regular rings, and Boolean algebras.
• Complemented zero-divisor graphs and Boolean rings
• On directed zero-divisor graphs of finite rings
• Cancellative commutative semigroups
• CYCLES AND SYMMETRIES OF ZERO-DIVISORS
• The Zero-Divisor Graphs Which Are Uniquely Determined By Neighborhoods
• Zero-Divisor Semigroups and Some Simple Graphs

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