On the planarity, genus and crosscap of new extension of zero-divisor graph of commutative rings

DOI10.1080/09728600.2022.2058437zbMath1487.05122OpenAlexW4224300912MaRDI QIDQ5074888

Nadeem ur Rehman, Mohd. Nazim, K. Selvakumar

Publication date: 10 May 2022

Published in: AKCE International Journal of Graphs and Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/09728600.2022.2058437

zbMATH Keywords

genuszero-divisor graphcrosscapextended zero-divisor graph

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Structure of finite commutative rings (13M05) General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) (13A70)

Related Items (1)

On the genus of extended zero-divisor graph of commutative rings

Cites Work

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• Projective total graphs of commutative rings
• Rings whose total graphs have genus at most one
• The total graph and regular graph of a commutative ring
• Zero-divisor graphs of genus one
• Classification of rings with projective zero-divisor graphs
• The total graph of a commutative ring
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• Beck's coloring of a commutative ring
• On the zero-divisor graph of a commutative ring
• Classification of rings with toroidal and projective coannihilator graph
• Classification of rings with crosscap two class of graphs
• Planar, outerplanar, and toroidal graphs of the generalized zero-divisor graph of commutative rings
• On the Genus of the Total Graph of a Commutative Ring
• On a New Extension of the Zero-Divisor Graph
• Classification of Rings with Genus One Zero-Divisor Graphs

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