dc.contributor.advisor Rasmussen, Craig W. dc.contributor.author Florkowski, Stanley F. dc.date.accessioned 2012-03-14T17:39:35Z dc.date.available 2012-03-14T17:39:35Z dc.date.issued 2008-12 dc.identifier.uri http://hdl.handle.net/10945/3852 dc.description.abstract In 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.uri http://archive.org/details/spectralgraphory109453852 dc.format.extent xiv, 53 p. en_US dc.publisher Monterey, California. Naval Postgraduate School en_US dc.rights This 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.lcsh Graph theory en_US dc.subject.lcsh Matrices en_US dc.title Spectral graph theory of the Hypercube en_US dc.type Thesis en_US dc.contributor.secondreader Gera, Ralucca M. dc.contributor.corporate Naval Postgraduate School (U.S.) dc.contributor.department Applied Mathematics dc.description.service US Army (USA) author. en_US dc.identifier.oclc 300322717 etd.thesisdegree.name M.S. en_US etd.thesisdegree.level Masters en_US etd.thesisdegree.discipline Applied Mathematics en_US etd.thesisdegree.grantor Naval Postgraduate School en_US etd.verified no en_US
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