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Results on minimum skew rank of matrices described by a graph
| Content Provider | Semantic Scholar |
|---|---|
| Author | DeLoss, Laura |
| Copyright Year | 2009 |
| Abstract | The minimum skew rank of a finite, simple, undirected graph G over a field F of characteristic not equal to 2 is defined to be the minimum possible rank of all skew-symmetric matrices over F whose i, j-entry is nonzero if and only if there exists an edge {i, j} in the graph G. The problem of determining the minimum skew rank of a graph arose after extensive study of the minimum (symmetric) rank problem. This thesis gives a background of techniques used to find minimum skew rank first developed by the IMA-ISU research group on minimum rank [9], proves cut-vertex reduction of a graph realized by a skew-symmetric matrix, and proves there is a bound for minimum skew rank created by the skew zero forcing number. The result of cut-vertex reduction is used to calculate the minimum skew ranks of families of coronas, and the minimum skew ranks of multiple other families of graphs are also computed. |
| File Format | PDF HTM / HTML |
| DOI | 10.31274/etd-180810-2409 |
| Alternate Webpage(s) | http://orion.math.iastate.edu/dept/thesisarchive/MS/DeLossMSSp09.pdf |
| Alternate Webpage(s) | https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1504&context=etd&httpsredir=1&referer= |
| Alternate Webpage(s) | https://doi.org/10.31274/etd-180810-2409 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
