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Spectra of graphs : theory and application
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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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An Arrow-Hurwicz-Uzawa type flow as least squares solver for network linear equations
TL;DR: A discrete-time distributed algorithm developed by Euler’s method, converging exponentially to the least squares solution at the node states with suitable step size and graph conditions is developed.
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Estrada index and Chebyshev polynomials
TL;DR: In this paper, the Estrada index of a graph whose eigenvalues are λ 1, λ 2, λ 3, ν n, ν 4, ξ 5, and ν 6 is approximated to ∑ i = 1 n e λ i.
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A note on the spectral characterization of θ-graphs
TL;DR: In this paper, it was shown that any θ-graph G is determined by the spectrum (the multiset of eigenvalues) except possibly when it contains a unique 4-cycle.
More Upper Bounds for the Incidence Energy
TL;DR: In this article, the first Zagreb index was used to obtain upper bounds for the incidence energy of a graph, which is defined as the sum of the singular values of the incidence matrix.
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Complete spectrum of the stochastic master equation for random walks on treelike fractals
TL;DR: In this article, the authors studied random walks on a family of treelike regular fractals with a trap fixed on a central node and obtained all the eigenvalues and their corresponding multiplicities for the associated stochastic master equation.