Directed Graphs of the Finite Tropical Semiring

Abstract

The focus of this paper lies at the intersection of the fields of tropical algebra and graph theory. In particular the interaction between tropical semirings and directed graphs is investigated. Originally studied in [7], the directed graph of a ring is useful in identifying properties within the algebraic structure of a ring. This work builds off the research done by [2, 5, 1] in constructing directed graphs from rings. However, we will investigate the relationship $(x , y ) → ({min}(x , y ), x + y )$ as defined by the operations of tropical algebra and applied to tropical semirings.

Publication
In Rose-Hulman Undergraduate Math Journal
Mike Janssen, Ph.D.
Mike Janssen, Ph.D.
Associate Professor of Mathematics

My research interests include commutative algebra, the use and creation of open course materials, inquiry in the mathematics classroom, alternative assessment methods, and increasing justice, equity, and inclusion in the mathematics classroom.