Irreducible Divisor Graphs in Commutative Rings with Zero Divisors

Abstract

In their article “Irreducible Divisor Graphs”, Coykendall and Maney (2007 Coykendall , J. , Maney , J. ( 2007 ). Irreducible divisor graphs . Comm. Alg. 35 : 885 – 895 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) introduced the idea of irreducible divisor graphs of elements of a domain. We generalize this concept to commutative rings with zero divisors. In particular, the interplay of unique factoring and connected/complete graphs is explored. The diameter and girth of such graphs are also briefly discussed.