# DisCoMath Seminar: Failed Positive Semidefinite Zero Forcing

Event Image

Discrete & Computational Math Seminar (DisCoMath)
Failed Positive Semidefinite Zero Forcing

Yutong Wu
Computational Mathematics BS Student
School of Mathematical Sciences, RIT

Abstract
:

Given a simple, undirected graph G, consider each vertex in V(G) as either “filled” or “unfilled”. Let S be the set of vertices that are filled. The positive semidefinite zero forcing rule is as follows:

• Consider each component of G−S.
• For each component Gi of G−S, consider Gi+A, where A is the set neighbors of the vertices in Gi from S.
• Apply zero forcing color change rule to Gi+A. That is, an unfilled vertex v is forced to be filled if it is the only unfilled neighbor of a filled vertex.
• Update S and repeat.

The maximum size of a set of filled vertices that fails to fill all vertices of G while applying the positive semidefinite zero forcing rule, denoted by F+(G), is called the failed positive semidefinite zero forcing number. We will discuss the parameter F+(G) for different types of graphs, as well as characterization of graphs with large F+(G) and graphs with small F+(G).

Intended Audience:

Keep up with DisCoMath Seminars on the DisCoMathS webpage.
To request an interpreter, please visit myaccess.rit.edu

Contact
Brendan Rooney
##### Event Snapshot
###### When and Where
November 12, 2021
2:30 pm - 3:30 pm
Room/Location: 2305
###### Who

This is an RIT Only Event

No

research