PPW Inequality on Graphs

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Momenzadeh, Omid | 2019

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 54208 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Daneshgar, Amir; Javadi Joratani, Ramin
Abstract:
The ratio of the two first non-trivial Dirichlet eigenvalues is the subject of the Payne-Polya-Weinburger Conjecture and Inequality. The PPW Conjecture was proven by M. Ashbaugh and R. Benguria. Ashbaugh and Benguria later proved a similar result for domains on the n-sphere. On the other hand, discrete counterparts of universal inequalities from (continuous) have been studied in the graph theory setting. This thesis surveys results related to the PPW inequality on graphs
Keywords:
Graph Theory ; Isoperimetric Inequality ; Spectral Geometry ; Payne-Polya-Weinburger (PPW)Inequality

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