On zero divisor graphs (Q2895447)

The paper under review gives a rather comprehensive survey on the recently developed active area of research on the zero-divisor graphs of commutative rings. The authors survey the research conducted on zero divisor graphs, with a focus on zero divisor graphs determined by equivalence classes of zero divisors of a commutative ring \(R\). In particular, they consider the problem of classifying star graphs with any finite number of vertices. They study the pathology of a zero divisor graph in terms of cliques, they investigate when the clique and chromatic numbers are equal, and they show that the girth of a Noetherian ring, if finite, is 3. Finally, they introduce a graph for modules that is useful for studying zero divisor graphs of trivial extensions.NEWLINENEWLINEThis well-written paper concludes with a number of interesting examples and applications. As a comment, readers who are interested in this paper might also wish to read the two other surveys which can be found at [\textit{D. F. Anderson, M. C. Axtell} and \textit{J. A. Stickles}, ``Zero-divisor graphs in commutative rings'', Commutative algebra. Noetherian and non-Noetherian perspectives. New York, NY: Springer. 23-45 (2011; Zbl 1225.13002)] and [\textit{H. M. Maimani, M. R. Pournaki, A. Tehranian} and \textit{S. Yassemi}, ``Graphs attached to rings revisited'', Arab. J. Sci. Eng. 36, No. 6, 997--1011 (2011)].NEWLINENEWLINEFor the entire collection see [Zbl 1237.13006].