Missouri Journal of Mathematical Sciences

Book Thickness of Planar Zero Divisor Graphs

Thomas McKenzie and Shannon Overbay

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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.

Article information

Source
Missouri J. Math. Sci., Volume 27, Issue 1 (2015), 2-9.

Dates
First available in Project Euclid: 3 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1449161362

Digital Object Identifier
doi:10.35834/mjms/1449161362

Mathematical Reviews number (MathSciNet)
MR3431110

Zentralblatt MATH identifier
1331.05106

Subjects
Primary: 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]
Secondary: 13M05: Structure

Keywords
book thickness zero divisor graphs commutative rings

Citation

McKenzie, Thomas; Overbay, Shannon. Book Thickness of Planar Zero Divisor Graphs. Missouri J. Math. Sci. 27 (2015), no. 1, 2--9. doi:10.35834/mjms/1449161362. https://projecteuclid.org/euclid.mjms/1449161362


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