Author: Ouyang, Chen
Title: Spectral hypergraph theory via tensors
Advisors: Qi, Liqun (AMA)
Li, Xun (AMA)
Degree: Ph.D.
Year: 2018
Subject: Hong Kong Polytechnic University -- Dissertations
Calculus of tensors
Department: Department of Applied Mathematics
Pages: xvi, 87 pages : illustrations
Language: English
Abstract: The thesis is devoted to a few problems on spectral hypergraphs theory via the adjacency tensor, Laplacian tensor and signless Laplacian tensor of a hypergraph. These problems are analogy and generalization of problems usually concerned in spectral graph theory. Three topics are included: 1. Characterization of uniform hypergraphs with largest spectral radii under certain conditions. 2. The property of symmetric spectrum for uniform hypergraphs with applications. 3. Properties on the spectra of non-uniform and general hypergrpahs. For the first topic, two types of connected hypergraphs with fixed vertex number and cyclomatic number called unicyclic and bicyclic hypergraphs are studied. By combining recent developed spectral techniques, the first five hypergraphs with largest spectral radii among all unicyclic hypergraphs and the first three over all bicyclic hypergraphs are determined, together with two orderings of the corresponding hypergraphs. For topic 2, we investigate the newly introduced odd-colorable hypergraphs and employ their symmetric spectra to obtain conditions for a uniform hypergraph to have equal Laplacian spectrum and signless Laplacian spectrum. For the last topic, some spectral bounds in terms of graph invariants are extended from uniform case to general hypergraphs, and a new way is found to bound the spectral radius from below for a special class of non-uniform hypergraphs. Moreover, the property of symmetric spectrum for general hypergraphs is investigated. Equivalent conditions are extened from uniform case to general case. Besides, the capability of a non-uniform hypergraph to have symmetric (H-)spectrum, equal Laplacian (H-)spectrum (spectral radius) and signless Lapalcian (H-)spectrum (spectral radius) is discussed.
Rights: All rights reserved
Access: open access

Files in This Item:
File Description SizeFormat 
991022165758203411.pdfFor All Users859.94 kBAdobe PDFView/Open

Copyright Undertaking

As a bona fide Library user, I declare that:

  1. I will abide by the rules and legal ordinances governing copyright regarding the use of the Database.
  2. I will use the Database for the purpose of my research or private study only and not for circulation or further reproduction or any other purpose.
  3. I agree to indemnify and hold the University harmless from and against any loss, damage, cost, liability or expenses arising from copyright infringement or unauthorized usage.

By downloading any item(s) listed above, you acknowledge that you have read and understood the copyright undertaking as stated above, and agree to be bound by all of its terms.

Show full item record

Please use this identifier to cite or link to this item: