## Missouri Journal of Mathematical Sciences

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

### Book Thickness of Planar Zero Divisor Graphs

Thomas McKenzie and Shannon Overbay

#### 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