Spectral Theory for Directed Graphs

The Hong Kong University of Science and Technology
Department of Computer Science and Engineering

Final Year Thesis Oral Presentation

Title: "Spectral Theory for Directed Graphs"

by

Mr. CAO Junhong


Abstract:

This final year thesis is on spectral theory in directed graphs. It checks 
several basic theorems and lemmas to search for potential gaps. Finally 
the attention comes to expander mixing lemma, while the lemma is well 
known in regular undirected graphs. The case for irregular undirected 
graphs and regular directed graphs are also found in references. The 
initial attempt is to find a similar conclusion in general irregular 
directed graphs. Though it should hold, it appears to be very difficult. 
Then a special case of irregular directed graphs, Eulerian graphs, where 
the in-degree and out-degree of each vertex are equal, is researched 
instead. And the conclusion for this case is proved.


Date                 : 30 April 2016 (Saturday)

Time                 : 10:15am to 11:00am

Venue                : Room 5510 (lift 25/26)

Advisor              : Dr. Ke YI

2nd Reader           : Prof. Cunsheng DING