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Tying The Knot: Applications Of Topology To Chemistry, Tarini S. Hardikar
Tying The Knot: Applications Of Topology To Chemistry, Tarini S. Hardikar
Honors Theses
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 …
On Property Pm,N And Some Applications To Graph Theory, Nancy Gaston
On Property Pm,N And Some Applications To Graph Theory, Nancy Gaston
Senior Scholar Papers
An intriguing concept in convexity theory is the characterization of sets having property Pm,n. A set is said to satisfy property Pm,n if for any collection of m arbitrary points at least n of the (m, 2) line segments determined by the points is contained in the given set. Valentine did the initial work with property P3,1, showing that a set with this property could be expressed as the union of 3 or fewer convex sets. This work was extended by Kay and Guay, who worked with the more general property Pm,n _ Convex: sets and graph theory were linked …