Book Thickness of Planar Zero Divisor Graphs

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.