Structure in Zero-Divisor Graphs of Commutative Rings

Author

Philip S. Livingston, University of Tennessee - Knoxville

Date of Award

12-1997

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

David F. Anderson

Committee Members

Robert Daverman, Carl G. Wagner

Abstract

In this research, we associate a graph in a natural way with the zero-divisors of a commutative ring. We endeavor to characterize various attributes of the graph, including connectivity, diameter, and symmetry. In exploring symmetry in the graph, we examine the automorphism group of the graph, and provide a complete characterization for the rings Z_N. Secondly, we seek ring-theoretic properties which may be described in terms of the associated zero-divisor graph. These include, among other results, a strong relationship between finite local rings and graphs admitting a vertex connected to every other vertex.

Recommended Citation

Livingston, Philip S., "Structure in Zero-Divisor Graphs of Commutative Rings. " Master's Thesis, University of Tennessee, 1997.
https://trace.tennessee.edu/utk_gradthes/1803