Bounding the Forcing Number of a Graph

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dc.contributor.advisorHicks, Illya V
dc.contributor.committeeMemberTapia, Richard A
dc.contributor.committeeMemberZhang, Yin
dc.creatorDavila, Randy R
dc.date.accessioned2016-01-07T17:28:35Z
dc.date.available2016-01-07T17:28:35Z
dc.date.created2015-05
dc.date.issued2015-04-16
dc.date.submittedMay 2015
dc.date.updated2016-01-07T17:28:36Z
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.
dc.format.mimetypeapplication/pdf
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>.
dc.identifier.urihttps://hdl.handle.net/1911/87761
dc.language.isoeng
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.
dc.subjectZero Forcing Number
dc.subjectk-Forcing Number
dc.titleBounding the Forcing Number of a Graph
dc.typeThesis
dc.type.materialText
thesis.degree.departmentComputational and Applied Mathematics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Arts
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