Print Email Facebook Twitter On the Dual of the Lovász Theta Prime Number for the Disjunctive Product of Graphs Title On the Dual of the Lovász Theta Prime Number for the Disjunctive Product of Graphs Author van der Waal, Leon (TU Delft Electrical Engineering, Mathematics and Computer Science) Contributor de Laat, D. (mentor) Janssens, B. (graduation committee) Degree granting institution Delft University of Technology Programme Applied Mathematics Date 2023-08-09 Abstract The Lovász theta function, and the variants of it given by Schrijver and Szegedy are upper bounds on the independence number of a graph. These functions play an important role in several optimization problems, such as the Cohn-Elkies bound for optimal sphere packing densities.This thesis covers the properties of these functions. The main focus of this thesis is the multiplicity of Schrijver's variant. A construction for optimal solutions to the dual problem of this function for the disjunctive graph product is proposed, and its generality is studied. It is shown that for abelian Cayley graphs, the Lovász theta function, and its variants reduce a linear program. Using properties of Fourier analysis an upper bound is given on the minimal gap between the largest and least eigenvalues of optimal solutions to the dual of Schrijver's variant. This, along with numerical results, suggests that the proposed construction is more likely to hold when abelian Cayley graphs are sparse. Subject OptimizationGraph theorySemidefinite programming To reference this document use: http://resolver.tudelft.nl/uuid:883e3ba8-3a57-4757-8493-1a5a8cf1519f Part of collection Student theses Document type bachelor thesis Rights © 2023 Leon van der Waal Files PDF BEP_Leon_van_der_Waal.pdf 874.36 KB Close viewer /islandora/object/uuid:883e3ba8-3a57-4757-8493-1a5a8cf1519f/datastream/OBJ/view