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Spectra of graphs : theory and application
TLDR
The Spectrum and the Group of Automorphisms as discussed by the authors have been used extensively in Graph Spectra Techniques in Graph Theory and Combinatory Applications in Chemistry an Physics. But they have not yet been applied to Graph Spectral Biblgraphy.Abstract:
Introduction. Basic Concepts of the Spectrum of a Graph. Operations on Graphs and the Resulting Spectra. Relations Between Spectral and Structural Properties of Graphs. The Divisor of a Graph. The Spectrum and the Group of Automorphisms. Characterization of Graphs by Means of Spectra. Spectra Techniques in Graph Theory and Combinatories. Applications in Chemistry an Physics. Some Additional Results. Appendix. Tables of Graph Spectra Biblgraphy. Index of Symbols. Index of Names. Subject Index.read more
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Comparison between Kirchhoff index and the Laplacian-energy-like invariant
TL;DR: In this article, the Kirchhoff index and the Laplacian energy-like invariant of a connected graph of order n were defined, and sufficient conditions under which LEL > Kf holds.
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The problem of deficiency indices for discrete Schrödinger operators on locally finite graphs
TL;DR: In this article, it was shown that the deficiency indices of any discrete Schrodinger operator acting on a simple tree are either null or infinite, and that all deterministic discreteSchrodinger operators which act on a random tree are almost surely self-adjoint.
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Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs☆
Peter E. Müller,Peter Stollmann +1 more
TL;DR: In this paper, the integrated density of states of the Dirichlet Laplacian is found to exhibit a Lifshits tail at the lower spectral edge, while that of the Neumann LaPLacian shows a van Hove asymptotics, which results from the percolating cluster.
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Random Graphs and Social Networks: An Economics Perspective
TL;DR: This review of current research on networks explores a number of examples to assess the potential of recent research on random graphs with arbitrary degree distributions in accommodating more general behavioral motivations for social network formation and concludes with an assessment of observable consequences of optimizing behavior in networks for the purpose of estimation.
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Q-integral graphs with edge-degrees at most five
Slobodan K. Simić,Zoran Stanić +1 more
TL;DR: This work considers the problem of determining the Q-integral graphs, i.e. the graphs with integral signless Laplacian spectrum, and finds all such graphs with maximum edge-degree 4, and obtains only partial results for the next natural case.