Physical Sciences and Mathematics Commons^™

Tropical Arithmetics And Dot Product Representations Of Graphs, Nicole Turner

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In tropical algebras we substitute min or max for the typical addition and then substitute addition for multiplication. A dot product representation of a graph assigns each vertex of the graph a vector such that two edges are adjacent if and only if the dot product of their vectors is greater than some chosen threshold. The resultS of creating dot product representations of graphs using tropical algebras are examined. In particular we examine the tropical dot product dimensions of graphs and establish connections to threshold graphs and the threshold dimension of a graph.