## Oral Session 02

### Spectral Properties of a Class of Bipartite Graphs

CSU 284

#### Start Date

21-4-2008 8:00 AM

#### End Date

21-4-2008 10:00 AM

#### Student's Major

Mathematics and Statistics

#### Student's College

Science, Engineering and Technology

In-Jae Kim

#### Mentor's Department

Mathematics and Statistics

#### Mentor's College

Science, Engineering and Technology

#### Description

To study dynamical systems, graphs are often used to capture the interactions among their components. The dynamics of the graphs can be described by associated matrices. The eigenvalues and eigenvectors of the matrices play a significant role in the study of these dynamical systems and their applications. For example, the search engine "Google" uses an eigenvalue and its corresponding eigenvector to rank websites in the World Wide Web. In this project, we investigated eigenvalues and eigenvectors of the adjacency matrices of bipartite graphs. Since it is extremely difficult to analyze all possible spectral properties of general bipartite graphs, we focused on bipartite graphs with a special structure. For that class of bipartite graphs, we have a complete description of eigenvalues and eigenvectors.

#### Share

COinS

Apr 21st, 8:00 AM Apr 21st, 10:00 AM

Spectral Properties of a Class of Bipartite Graphs

CSU 284

To study dynamical systems, graphs are often used to capture the interactions among their components. The dynamics of the graphs can be described by associated matrices. The eigenvalues and eigenvectors of the matrices play a significant role in the study of these dynamical systems and their applications. For example, the search engine "Google" uses an eigenvalue and its corresponding eigenvector to rank websites in the World Wide Web. In this project, we investigated eigenvalues and eigenvectors of the adjacency matrices of bipartite graphs. Since it is extremely difficult to analyze all possible spectral properties of general bipartite graphs, we focused on bipartite graphs with a special structure. For that class of bipartite graphs, we have a complete description of eigenvalues and eigenvectors.

#### Recommended Citation

Watts, Brendon. "Spectral Properties of a Class of Bipartite Graphs." Undergraduate Research Symposium, Mankato, MN, April 21, 2008.
https://cornerstone.lib.mnsu.edu/urs/2008/oral-session-02/6