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Spectral Theory of Infinite Quantum Graphs [PDF]
Annales Henri Poincaré, 2018 We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a close connection
Exner, Pavel +3 more
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A Few Examples and Counterexamples in Spectral Graph Theory
Discussiones Mathematicae Graph Theory, 2020 We present a small collection of examples and counterexamples for selected problems, mostly in spectral graph theory, that have occupied our minds over a number of years without being completely resolved.
Stevanović Dragan +2 more
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Spectral graph theory : from practice to theory [PDF]
, 2020 Graph theory is the area of mathematics that studies networks, or graphs. It arose from the need to analyse many diverse network-like structures like road networks, molecules, the Internet, social networks and electrical networks.
Farrugia, Alexander
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Shapes of Uncertainty in Spectral Graph Theory [PDF]
IEEE Transactions on Information Theory, 2020 We present a flexible framework for uncertainty principles in spectral graph theory. In this framework, general filter functions modeling the spatial and spectral localization of a graph signal can be incorporated. It merges several existing uncertainty relations on graphs, among others the Landau-Pollak principle describing the joint admissibility ...
Wolfgang Erb
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Spectral theory of quantum graphs
, 2012 Diese Arbeit beinhaltet Untersuchungen von Spektralproblemen für Quantengraphen mit Potential. Einerseits analysieren wir die quantitative Abhängigkeit der Eigenwerte des Schrödingeroperators vom Potential. Andererseits verallgemeinern wir gewisse elementare Identitäten von der eindimensionalen Streutheorie auf Quantengraphen.
Semra Demirel
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Geary’s c and Spectral Graph Theory: A Complement
Mathematics, 2023 Spatial autocorrelation, which describes the similarity between signals on adjacent vertices, is central to spatial science, and Geary’s c is one of the most-prominent numerical measures of it.
Hiroshi Yamada
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Spectral theory of the non-backtracking Laplacian for graphs [PDF]
Discrete Mathematics, 2022 We introduce a non-backtracking Laplace operator for graphs and we investigate its spectral properties. With the use of both theoretical and computational techniques, we show that the spectrum of this operator captures several structural properties of the graph in a more precise way than the classical operators that have been studied so far in the ...
Jürgen Jost +2 more
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Spectrum and energy of the Sombor matrix [PDF]
Vojnotehnički Glasnik, 2021 Introduction/purpose: The Sombor matrix is a vertex-degree-based matrix associated with the Sombor index. The paper is concerned with the spectral properties of the Sombor matrix. Results: Equalities and inequalities for the eigenvalues of the Sombor
Ivan Gutman
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Spectral recognition of graphs [PDF]
Yugoslav Journal of Operations Research, 2012 At some time, in the childhood of spectral graph theory, it was conjectured that non-isomorphic graphs have different spectra, i.e. that graphs are characterized by their spectra.
Cvetković Dragoš
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