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2016 Cut structures in zero-divisor graphs of commutative rings
M. Axtell, N. Baeth, J. Stickles
J. Commut. Algebra 8(2): 143-171 (2016). DOI: 10.1216/JCA-2016-8-2-143

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.

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M. Axtell. N. Baeth. J. Stickles. "Cut structures in zero-divisor graphs of commutative rings." J. Commut. Algebra 8 (2) 143 - 171, 2016. https://doi.org/10.1216/JCA-2016-8-2-143

Information

Published: 2016
First available in Project Euclid: 10 June 2016

zbMATH: 1346.13011
MathSciNet: MR3510916
Digital Object Identifier: 10.1216/JCA-2016-8-2-143

Subjects:
Primary: 13A99

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

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Vol.8 • No. 2 • 2016
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