On the Planarity of Extended Zero-Divisor Graphs of Local Rings

On the Planarity of Extended Zero-Divisor Graphs of Local Rings

Let R be a commutative ring with unity 1≠0. Recently Bennis et al. defined the concept of extended zero-divisor graph Γ¯R by considering the vertex set VΓ¯R=Z∗R and any two vertices x and y are adjacent if there exist positive integers m and n, such that xmyn=0 with xm≠0 and yn≠0. The main object...

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Bibliographic Details
Main Authors: Abbasi, M.S (Author), Alameri, A. (Author), Binyamin, M.A (Author), Chaudry, S.A (Author)
Format: Article
Language:English
Published: Hindawi Limited 2022
Subjects:
Commutative ring
Graph theory
Local ring
Planarity
Positive integers
Property
Vertex set
Zero-divisor graphs
Online Access:View Fulltext in Publisher
Description
Summary:Let R be a commutative ring with unity 1≠0. Recently Bennis et al. defined the concept of extended zero-divisor graph Γ¯R by considering the vertex set VΓ¯R=Z∗R and any two vertices x and y are adjacent if there exist positive integers m and n, such that xmyn=0 with xm≠0 and yn≠0. The main objective of this article is to check the planar property of extended zero-divisor graphs. Also, a complete list of local rings up to order 27 with planar extended zero-divisor graphs has been collected. © 2022 Muhammad Ahsan Binyamin et al.
ISBN:1024123X (ISSN)
DOI:10.1155/2022/4183107

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