DisCoMath Seminar: Failed Positive Semidefinite Zero Forcing
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:
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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).
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Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
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