## Journal of Commutative Algebra

### Cut structures in zero-divisor graphs of commutative rings

#### Abstract

Zero-divisor graphs, and more recently, compressed zero-divisor graphs are well represented in the commutative ring literature. In this work, we consider various cut structures, sets of edges or vertices whose removal disconnects the graph, in both compressed and non-compressed zero-divisor graphs. In doing so, we connect these graph-theoretic concepts with algebraic notions and provide realization theorems of zero-divisor graphs for commutative rings with identity.

#### Article information

Source
J. Commut. Algebra, Volume 8, Number 2 (2016), 143-171.

Dates
First available in Project Euclid: 10 June 2016

https://projecteuclid.org/euclid.jca/1465574595

Digital Object Identifier
doi:10.1216/JCA-2016-8-2-143

Mathematical Reviews number (MathSciNet)
MR3510916

Zentralblatt MATH identifier
1346.13011

Subjects
Primary: 13A99: None of the above, but in this section

#### Citation

Axtell, M.; Baeth, N.; Stickles, J. Cut structures in zero-divisor graphs of commutative rings. J. Commut. Algebra 8 (2016), no. 2, 143--171. doi:10.1216/JCA-2016-8-2-143. https://projecteuclid.org/euclid.jca/1465574595

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