Idempotent Divisor Graph of Commutative Ring: Idempotent Divisor Graph

Husam Q.  Mohammad; Nazar H.  Shuker

doi:10.24996/ijs.2022.63.2.21

Authors

Husam Q. Mohammad Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq
Nazar H. Shuker Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.2.21

Keywords:

Idempotent Elements, Zero Divisor Graph, Idempotent Divisor Graph, Planar Graph

Abstract

This work aims to introduce and to study a new kind of divisor graph which is called idempotent divisor graph, and it is denoted by . Two non-zero distinct vertices v₁ and v₂ are adjacent if and only if , for some non-unit idempotent element . We establish some fundamental properties of , as well as it’s connection with . We also study planarity of this graph.