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Mean Eigenvalue Counting Function Bound for Laplacians on Random Networks

Spectral graph theory widely increases the interests in not only discovering new properties of well known graphs but also proving the well known properties for the new type of graphs. In fact all spectral properties of proverbial graphs are not acknowledged to us and in other hand due to the structure of nature, new classes of graphs are required to explain the phenomena around us and the spectral properties of these graphs can tell us more about the structure of them. These both themes are the body of our work here. We introduce here three models of random graphs and show that the eigenvalue counting function of Laplacians on these graphs has exponential decay bound. Since our methods heavily depend on the first nonzero eigenvalue of Laplacian, we study also this eigenvalue for the graph in both random and nonrandom cases.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-qucosa-159578
Date22 January 2015
CreatorsSamavat, Reza
ContributorsTU Chemnitz, Fakultät für Mathematik, Prof. Dr. Peter Stollmann, Prof. Dr. Peter Müller
PublisherUniversitätsbibliothek Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:doctoralThesis
Formatapplication/pdf, text/plain, application/zip

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