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dc.contributor.advisorRusnak, Lucas
dc.contributor.authorRobinson, Ellen Beth ( )
dc.date.accessioned2016-01-20T19:49:26Z
dc.date.available2016-01-20T19:49:26Z
dc.date.issued2015-12
dc.identifier.citationRobinson, E. B. (2015). A new interpretation of the Matrix Tree Theorem using weak walk contributions and circle activation (Unpublished thesis). Texas State University, San Marcos, Texas.
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/5945
dc.descriptionPresented to the Honors Committee of Texas State University In Partial Fulfillment of the Requirements For Graduation in the Honors College, December 2015.en_US
dc.description.abstractThis thesis provides an alternate proof of the Matrix Tree Theorem by shifting the focus to oriented incidences. We examine the weak walk contributors from the de-terminant of the Laplacian matrix of oriented graphs and classify them according to similar circle structures attained through circle activation. The members of each of these contribution classes form an alternating rank-signed Boolean lattice in which all members cancel. We then restrict our contributors to those corresponding to a given cofactor Lij and demonstrate that those contributors that no longer cancel are in one-to-one correspondence with the spanning trees of the graph. These results allow for possible extension into examining tree-counts in signed graphs and oriented hypergraphs.en_US
dc.formatText
dc.format.extent34 pages
dc.format.medium1 file (.pdf)
dc.language.isoen
dc.subjectGraphsen_US
dc.subjectMatrixen_US
dc.subjectTreesen_US
dc.subjectCombinatoricsen_US
dc.subjectGraph Theoryen_US
dc.subjectSigned graphsen_US
dc.titleA New Interpretation of the Matrix Tree Theorem Using Weak Walk Contributions and Circle Activationen_US
txstate.documenttypeThesis
dc.contributor.committeeMemberFerrero, Daniela
thesis.degree.departmentHonors College
thesis.degree.disciplineMathematics
thesis.degree.grantorTexas State University
txstate.departmentHonors College


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