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dc.contributor.advisorRasmussen, Craig W.
dc.contributor.authorFlorkowski, Stanley F.
dc.date.accessioned2012-03-14T17:39:35Z
dc.date.available2012-03-14T17:39:35Z
dc.date.issued2008-12
dc.identifier.urihttp://hdl.handle.net/10945/3852
dc.description.abstractIn Graph Theory, every graph can be expressed in terms of certain real, symmetric matrices derived from the graph, most notably the adjacency or Laplacian matrices. Spectral Graph Theory focuses on the set of eigenvalues and eigenvectors, called the spectrum, of these matrices and provides several interesting areas of study. One of these is the inverse eigenvalue problem of a graph, which tries to determine information about the possible eigenvalues of the real symmetric matrices whose pattern of nonzero entries is described by a given graph. A second area is the energy of a graph, defined to be the sum of the absolute values of the eigenvalues of the adjacency matrix of that graph. Here we explore these two areas for the hypercube Qn, which is formed recursively by taking the Cartesian product of Qn-1 with the complete graph on two vertices, K2. We analyze and compare several key ideas from the inverse eigenvalue problem for Qn, including the maximum multiplicity of possible eigenvalues, the minimum rank of possible matrices, and the number of paths that occur both as induced subgraphs and after deleting certain vertices. We conclude by deriving several equations for the energy of Qn.en_US
dc.description.urihttp://archive.org/details/spectralgraphory109453852
dc.format.extentxiv, 53 p.en_US
dc.publisherMonterey, California. Naval Postgraduate Schoolen_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.subject.lcshGraph theoryen_US
dc.subject.lcshMatricesen_US
dc.titleSpectral graph theory of the Hypercubeen_US
dc.typeThesisen_US
dc.contributor.secondreaderGera, Ralucca M.
dc.contributor.corporateNaval Postgraduate School (U.S.)
dc.contributor.departmentApplied Mathematics
dc.description.serviceUS Army (USA) author.en_US
dc.identifier.oclc300322717
etd.thesisdegree.nameM.S.en_US
etd.thesisdegree.levelMastersen_US
etd.thesisdegree.disciplineApplied Mathematicsen_US
etd.thesisdegree.grantorNaval Postgraduate Schoolen_US
etd.verifiednoen_US


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