Proper Colorings and p-Partite Structures of the Zero Divisor Graph

Authors

Anna Duane, Carlton CollegeFollow

Abstract

Let Γ(Zm) be the zero divisor graph of the ring Zm. In this paper we explore the p-partite structures of Γ(Zm), as well as determine a complete classification of the chromatic number of Γ(Zm). In particular, we explore how these concepts are related to the prime factorization of m.

Author Bio

Anna Duane is a senior math major at Carleton College in Northfield, Minnesota. I am currently taking part in the Budapest Semesters in Mathematics. The primary mathematical field I am interested in is combinatorial graph theory, which I intend to pursue eventually in graduate school. After graduation I plan to live and work in Washington, DC.

Faculty Sponsor

Mike Axtell

Recommended Citation

Duane, Anna (2006) "Proper Colorings and p-Partite Structures of the Zero Divisor Graph," Rose-Hulman Undergraduate Mathematics Journal: Vol. 7: Iss. 2, Article 16.
Available at: https://scholar.rose-hulman.edu/rhumj/vol7/iss2/16