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November 2015 Book Thickness of Planar Zero Divisor Graphs
Thomas McKenzie, Shannon Overbay
Missouri J. Math. Sci. 27(1): 2-9 (November 2015). DOI: 10.35834/mjms/1449161362

Abstract

Let $R$ be a finite commutative ring with identity. We form the zero divisor graph of $R$ by taking the nonzero zero divisors as the vertices and connecting two vertices, $x$ and $y$, by an edge if and only if $xy=0$. We establish that if the zero divisor graph of a finite commutative ring with identity is planar, then the graph has a planar supergraph with a Hamiltonian cycle. We also determine the book thickness of all planar zero divisor graphs.

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Thomas McKenzie. Shannon Overbay. "Book Thickness of Planar Zero Divisor Graphs." Missouri J. Math. Sci. 27 (1) 2 - 9, November 2015. https://doi.org/10.35834/mjms/1449161362

Information

Published: November 2015
First available in Project Euclid: 3 December 2015

zbMATH: 1331.05106
MathSciNet: MR3431110
Digital Object Identifier: 10.35834/mjms/1449161362

Subjects:
Primary: 05C10
Secondary: 13M05

Rights: Copyright © 2015 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.27 • No. 1 • November 2015
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