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

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

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.

Suggested Citation

  • Muhammad Ahsan Binyamin & Sheroz Alam Chaudry & Muhammad Salman Abbasi & Abdu Alameri & Ardashir Mohammadzadeh, 2022. "On the Planarity of Extended Zero-Divisor Graphs of Local Rings," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-4, March.
    • Handle: RePEc:hin:jnlmpe:4183107
    DOI: 10.1155/2022/4183107
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