Degree Type

Thesis

Date of Award

2009

Degree Name

Master of Science

Department

Mathematics

First Advisor

Leslie Hogben

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 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.

Copyright Owner

Laura Leigh Deloss

Language

en

Date Available

2012-04-28

File Format

application/pdf

File Size

33 pages

Included in

Mathematics Commons

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