We examine minimal sets of vertices which, when removed from a zero-divisor graph, separate the graph into disconnected subgraphs. We classify these sets for all direct products of Γ ∏Zni

Author Bio

Benjamin Coté just finished his degree in Mathematics from the University of Idaho. For his senior year, he studied in Hungary with the Budapest Semesters in Mathematics program. Next year he will attend the graduate program in mathematics at the University of California, Santa Barbara.

Caroline Ewing Graduated from Colorado College in the spring of 2010 with a B.A. in Mathematics. She is working Lake Powell for the summer.

Michael Huhn graduated from the University of St. Thomas in December 2009, with a B.A. in Mathematics. His future plans included Mathematics, whether teaching Mathematics or studying Mathematics at the PhD or Master's Level.

Chelsea M. Plaut attends the University of Tennessee, Knoxville, where she is pursuing a math major and a music minor. After attaining her bachelor's degree she plans to continue towards her master's at UT. Her future plans include obtaining a PhD in mathematics, teaching at the university level, and conducting research in her field of study.

Darrin Weber attends Millikin University in Decatur, IL, and will graduate in the spring of 2011 with an Applied Mathematics degree. He plans on attending graduate school to pursue a Ph.D. in theoretical mathematics.