## Oral Session 12

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

CSU 284A

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

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.

#### Share

COinS

Apr 5th, 9:00 AM Apr 5th, 10:30 AM

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