On the Planarity of Extended Zero-Divisor Graphs of Local Rings. (23rd March 2022) - Binyamin, Muhammad Ahsan; Chaudry, Sheroz Alam; Abbasi, Muhammad Salman; Alameri, Abdu
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.