On the essential graph of a commutative ring

DOI10.1142/S0219498817501328zbMath1367.13005MaRDI QIDQ5272573

Reza Nikandish, M. Bakhtyiari, Mohammad Javad Nikmehr

Publication date: 30 June 2017

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

zbMATH Keywords

chromatic numberclique numbercomplete graphzero-divisor graphessential annihilator graph

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Ideals and multiplicative ideal theory in commutative rings (13A15) Graph theory (05C99) Commutative ring extensions and related topics (13B99)

Related Items (12)

Perfect Nilpotent Graphs ⋮ Unnamed Item ⋮ Finite commutative ring with genus two essential graph ⋮ On the essential annihilating-ideal graph of commutative rings ⋮ Crosscap two of class of graphs from commutative rings ⋮ Generalized essential submodule graph of an \(R\)-module ⋮ Genus two nilpotent graphs of finite commutative rings ⋮ Unnamed Item ⋮ When the annihilator-ideal graph is planar or complete bipartite graph ⋮ The weakly zero-divisor graph of a commutative ring ⋮ On the compressed essential graph of a module over a commutative ring ⋮ A generalization of the zero-divisor graph for modules

Cites Work

• Unnamed Item
• Unnamed Item
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• The unit graph of a left Artinian ring
• The diameter of a zero divisor graph
• CYCLES AND SYMMETRIES OF ZERO-DIVISORS
• SOME RESULTS ON THE INTERSECTION GRAPHS OF IDEALS OF RINGS
• THE ANNIHILATOR IDEAL GRAPH OF A COMMUTATIVE RING
• On the Dot Product Graph of a Commutative Ring
• Domination number in the annihilating-ideal graphs of commutative rings
• On the Annihilator Graph of a Commutative Ring

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