Date of Award

2017

Document Type

Honors Thesis (Open Access)

Department

Colby College. Mathematics and Statistics Dept.

Advisor(s)

Dr. Scott A. Taylor

Abstract

Chirality (or handedness) is the property that a structure is “different” from its mirror image. Topology can be used to provide a rigorous framework for the notion of chirality. This project examines various types of chirality and discusses tools to detect chirality in graphs and knots. Notable theorems that are discussed in this work include ones that identify chirality using properties of link polynomials (HOMFLY polynomials), rigid vertex graphs, and knot linking numbers. Various other issues of chirality are explored, and some specially unique structures are discussed. This paper is borne out of reading Dr. Erica Flapan’s book, When Topology Meets Chemistry. It follows the structure of the book closely, and in a sense, tells the same story, but as a modern adaptation. Every uncited theorem and definition and fact is from this book.

The second part of this work focuses on using graph theory to better span molecular graphs. This part is significantly less explored, but nevertheless, presents some interesting prospects.

Keywords

topology, chemistry, chirality, knot theory, graph theory

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