Author

Ariel Rozen

Date of Award

2023

First Advisor

Timothy Susse

Second Advisor

Miha Habič

Abstract

The structure of groups and graphs, how they are associated with one another, and how to classify them, is a mathematical problem which has much room for further development. From any given graph, we consider the right angled Coxeter group which can be constructed from the graph, and from the RACG, the group of Outer Automorphisms that act on it. We can demonstrate that under proper circumstances the rank of Out0(WΓ) can be determined based exactly on how many separating intersections of links appear in Γ. We begin by introducing the necessary context of sets, group theory, and graph theory. We then cover what has been shown before, providing useful theorems for the goal of rank classification. Lastly, in the final chapter we go through several cases to demonstrate that in such cases the rank of Out0(WΓ) is indeed equal to the number of SILs on Γ.

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