Open AccessWhen zero-divisor graphs are divisor graphs
Author(s) -
Emad Abu Osba,
Osama Alkam
Publication year - 2017
Publication title -
turkish journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.454
H-Index - 27
eISSN - 1303-6149
pISSN - 1300-0098
DOI - 10.3906/mat-1601-102
Subject(s) - mathematics , zero divisor , combinatorics , commutative ring , graph , divisor (algebraic geometry) , discrete mathematics , commutative property
Let R be a finite commutative principal ideal ring with unity. In this article, we prove that the zero-divisor graph Γ(R) is a divisor graph if and only if R is a local ring or it is a product of two local rings with at least one of them having diameter less than 2. We also prove that Γ(R) is a divisor graph if and only if Γ(R[x]) is a divisor graph if and only if Γ(R[[x]]) is a divisor graph.
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