Date of Completion

4-20-2022

Degree Type

Honors Thesis

Discipline

Mathematics (MATH)

First Advisor

Blake Mellor

Abstract

The Double Handcuff and K4 graphs can be generalized to a single family of spatial graphs by adding a variable number of twists between two edges. We can identify spatial graphs by calculating a quotient of the fundamental quandle, known as an N-quandle, which is a spatial graph invariant. In this paper, we prove that the N-quandle associated with this family of spatial graphs is finite when all but two edges are given a label of 2, and the remaining two edges are assigned labels from the natural numbers. To prove that the N-quandle is finite, we produce Cayley graphs for each of the N-quandle components, providing corresponding proofs and analysis.

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