Title
Cut-structures in zero-divisor graphs of commutative rings
Department/School
Mathematics
Date
6-10-2016
Document Type
Article
Keywords
cut-structures, zero-divisor graphs
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.
Published in
Journal of Commutative Algebra
COinS
Citation/Other Information
Axtell, M., Baeth, N., & Stickles, J. (2016). Cut structures in zero-divisor graphs of commutative rings. Journal of Commutative Algebra. 8(2), 143-171. https://doi.org/10.1216/JCA-2016-8-2-143.