A New Interpretation of the Matrix Tree Theorem Using Weak Walk Contributions and Circle Activation

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dc.contributor.advisorRusnak, Lucas
dc.contributor.authorRobinson, Ellen Beth
dc.contributor.committeeMemberFerrero, Daniela
dc.date.accessioned2016-01-20T19:49:26Z
dc.date.available2016-01-20T19:49:26Z
dc.date.issued2015-12
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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent34 pages
dc.format.medium1 file (.pdf)
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 A new interpretation of the Matrix Tree Theorem using weak walk contributions and circle activation (Unpublished thesis).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://hdl.handle.net/10877/5945
dc.language.isoen
dc.subjectgraphs
dc.subjectmatrix
dc.subjecttrees
dc.subjectcombinatorics
dc.subjectgraph Theory
dc.subjectsigned graphs
dc.titleA New Interpretation of the Matrix Tree Theorem Using Weak Walk Contributions and Circle Activation
dc.typeThesis
thesis.degree.departmentHonors College
thesis.degree.disciplineMathematics
thesis.degree.grantorTexas State University

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