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

Muhammad Ahsan Binyamin, Sheroz Alam Chaudry, Muhammad Salman Abbasi, Abdu Alameri and Ardashir Mohammadzadeh

Mathematical Problems in Engineering, 2022, vol. 2022, 1-4

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 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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:4183107

DOI: 10.1155/2022/4183107

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