On the Planarity of Extended Zero-Divisor Graphs of Local Rings. (23rd March 2022)

• Record Type: Journal Article
• Authors: Binyamin, Muhammad Ahsan; Chaudry, Sheroz Alam; Abbasi, Muhammad Salman; Alameri, Abdu
• Other Names: Mohammadzadeh Ardashir Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2022(2022)
• Publication Date: 2022-03-23
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2022/4183107
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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 V Γ ¯ R = Z ∗ R and any two vertices x and y are adjacent if there exist positive integers m and n, such that x m y n = 0 with x m ≠ 0 and y n ≠ 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.