The effect of removing a 2-downer edge or a cut 2-downer edge triangle for an eigenvalue
Edges in the graph associated with a square matrix over a field may be classified as to how their removal affects the multiplicity of an identified eigenvalue. There are five possibilities: +2+2 (2-Parter); +1+1 (Parter); no change (neutral); −1-1 (downer); and −2-2 (2-downer). Especially, it is kno...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-03-01
|
| Series: | Special Matrices |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/spma-2022-0186 |
| Summary: | Edges in the graph associated with a square matrix over a field may be classified as to how their removal affects the multiplicity of an identified eigenvalue. There are five possibilities: +2+2 (2-Parter); +1+1 (Parter); no change (neutral); −1-1 (downer); and −2-2 (2-downer). Especially, it is known that 2-downer edges for an eigenvalue comprise cycles in the graph. We investigate the effect for the statuses of other edges or vertices by removing a 2-downer edge. Then, we investigate the change in the multiplicity of an eigenvalue by removing a cut 2-downer edge triangle. |
|---|---|
| ISSN: | 2300-7451 |