#### Event Title

### Minimum Rank, Zero Forcing Number and Network Propagation

#### Location

CSU 284A

#### Start Date

5-4-2011 9:00 AM

#### End Date

5-4-2011 10:30 AM

#### Student's Major

Mathematics and Statistics

#### Student's College

Science, Engineering and Technology

#### Mentor's Name

In-Jae Kim

#### Mentor's Department

Mathematics and Statistics

#### Mentor's College

Science, Engineering and Technology

#### Description

A graph consists of vertices and edges. An edge connects a pair of vertices. The minimum rank of a graph G is the smallest rank that can be achieved by a symmetric matrix whose graph is G. The computation of the minimum rank of a graph is equivalent to that of the maximum co-rank of the graph. It is know that the zero forcing number of a graph is an upper bound on the maximum co-rank of the graph. In this presentation we introduce the zero forcing number of a graph and its relation to the minimum rank of the graph, and show how we can use the zero forcing number in the study of network propagation.

Minimum Rank, Zero Forcing Number and Network Propagation

CSU 284A

A graph consists of vertices and edges. An edge connects a pair of vertices. The minimum rank of a graph G is the smallest rank that can be achieved by a symmetric matrix whose graph is G. The computation of the minimum rank of a graph is equivalent to that of the maximum co-rank of the graph. It is know that the zero forcing number of a graph is an upper bound on the maximum co-rank of the graph. In this presentation we introduce the zero forcing number of a graph and its relation to the minimum rank of the graph, and show how we can use the zero forcing number in the study of network propagation.

#### Recommended Citation

Chen, Moyang. "Minimum Rank, Zero Forcing Number and Network Propagation." *Undergraduate Research Symposium*, Mankato, MN, April 5, 2011.

https://cornerstone.lib.mnsu.edu/urs/2011/oral-session-12/4