Directed Graphs of Commutative Rings

Abstract. The directed graph of a commutative ring is a graph representation of its additive and multiplicative structure. Using the mapping (a, b) → (a + b, a · b) one can create a directed graph for every finite, commutative ring. We examine the properties of directed graphs of commutative rings, with emphasis on the information the graph gives about the ring. Acknowledgements: We would like to acknowledge the University of St. Thomas for making this research possible and Dr. Michael Axtell for his guidance throughout. Page 168 RHIT Undergrad. Math. J., Vol. 14, no.