Bounding the Forcing Number of a Graph

Simple item page
dc.contributor.advisorHicks, Illya Ven_US
dc.contributor.committeeMemberTapia, Richard Aen_US
dc.contributor.committeeMemberZhang, Yinen_US
dc.creatorDavila, Randy Ren_US
dc.date.accessioned2016-01-07T17:28:35Zen_US
dc.date.available2016-01-07T17:28:35Zen_US
dc.date.created2015-05en_US
dc.date.issued2015-04-16en_US
dc.date.submittedMay 2015en_US
dc.date.updated2016-01-07T17:28:36Zen_US
dc.description.abstractThe forcing number, denoted F(G), is an upper bound for the maximum nullity of all symmetric matrices with a sparsity pattern described by the simple graph G. Simple lower and upper bounds are δ ≤ F(G) where δ is the minimum degree and F (G) ≤ n − 1 where n is the order of the graph. This thesis provides improvements on the minimum degree lower bound in the case that G has girth of at least 5. In particular, it is shown that 2δ − 2 ≤ F (G) for graphs with girth of at least 5; this can be further improved when G has a small cut set. Further, this thesis also conjectures a lower bound on F(G) as a function of the girth, g, and δ.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationDavila, Randy R. "Bounding the Forcing Number of a Graph." (2015) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/87761">https://hdl.handle.net/1911/87761</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/87761en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectZero Forcing Numberen_US
dc.subjectk-Forcing Numberen_US
dc.titleBounding the Forcing Number of a Graphen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputational and Applied Mathematicsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
DAVILA-DOCUMENT-2015.pdf
Size:
237.1 KB
Format:
Adobe Portable Document Format
Download
License bundle
Now showing 1 - 2 of 2
No Thumbnail Available
Name:
PROQUEST_LICENSE.txt
Size:
5.84 KB
Format:
Plain Text
Description:
Download
No Thumbnail Available
Name:
LICENSE.txt
Size:
2.61 KB
Format:
Plain Text
Description:
Download
Collections
Rice University Theses and Dissertations