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

Abstract

Let R be a commutative ring with unity 1? 0. Recently Bennis et al. defined the concept of extended zero-divisor graph ? (R) by considering the vertex set V (? (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. e 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.