Local Rings with Genus Two Zero Divisor Graph

Abstract

To each commutative ring R we can associate a graph, the zero divisor graph of R, whose vertices are the zero divisors of R, and such that two vertices are adjacent if their product is zero. Presently, we enumerate the local finite commutative rings whose zero divisor graphs have orientable genus 2.

Key Words:

• Commutative algebra
• Finite rings
• Local rings
• Zero divisor graphs

2000 Mathematics Subject Classification:

• Primary 05C25
• Secondary 13H99
• 13M99

ACKNOWLEDGMENTS

This work was supported in part by the National Science Foundation under award number DMS-0552573. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the National Science Foundation.

Notes

Communicated by I. Swanson.