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New constructions of strongly regular graphs

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dc.contributor.authorLane-Harvard, Elizabeth, author
dc.contributor.authorPenttila, Tim, advisor
dc.contributor.authorGloeckner, Gene, committee member
dc.contributor.authorHulpke, Alexander, committee member
dc.contributor.authorPeterson, Chris, committee member
dc.date.accessioned2007-01-03T06:31:55Z
dc.date.available2007-01-03T06:31:55Z
dc.date.issued2014
dc.description.abstractThere are many open problems concerning strongly regular graphs: proving non-existence for parameters where none are known; proving existence for parameters where none are known; constructing more parameters where examples are already known. The work addressed in this dissertation falls into the last two categories. The methods used involve symmetry, geometry, and experimentation in computer algebra systems. In order to construct new strongly regular graphs, we rely heavily on objects found in finite geometry, specifically two intersection sets and generalized quadrangles, in which six independent successes occur. New two intersection sets are constructed in finite Desarguesian projective planes whose strongly regular graph parameters correspond to previously unknown and known ones. An infinite family of new two intersection sets is also constructed in finite projective spaces in 5 dimensions. The infinite family of strongly regular graphs have the same parameters as Paley graphs. Next, using the point graph of the classical GQ H(3,q2), q even, a new infinite family of strongly regular graphs is constructed. Then we generalize three infinite families of strongly regular graphs from large arcs in Desarguesian projective planes to the non-Desarguesian case. Finally, a construction of strongly regular graphs from ovoids of generalized quadrangles of Godsil and Hensel is applied to non-classical generalized quadrangles to obtain new families of strongly regular graphs.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierLaneHarvard_colostate_0053A_12414.pdf
dc.identifier.urihttp://hdl.handle.net/10217/83754
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectgeneralized quadrangle
dc.subjectstrongly regular graph
dc.titleNew constructions of strongly regular graphs
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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