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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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Networks in life: Scaling properties and eigenvalue spectra
Illés J. Farkas,Imre Derényi,Imre Derényi,Hawoong Jeong,Zoltán Néda,Zoltán Néda,Zoltán N. Oltvai,Erzsébet Ravasz,András Schubert,Albert-László Barabási,Tamás Vicsek +10 more
TL;DR: In this paper, the authors analyze growing networks ranging from collaboration graphs of scientists to the network of similar similarities among the various transcriptional proteins of living cells, and demonstrate the use of determining the eigenvalue spectra of sparse random graph models for the categorization of small measured networks.
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Spectral Determinant on Quantum Graphs
Eric Akkermans,Eric Akkermans,Alain Comtet,Jean Desbois,Gilles Montambaux,Christophe Texier,Christophe Texier +6 more
TL;DR: In this article, the spectral determinant of the Laplacian on finite graphs characterized by their number of vertices V and bonds B was studied. And the results were generalized to the case of graphs in a magnetic field.
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On the generalized adjacency, Laplacian and signless Laplacian spectra of the weighted edge corona networks
TL;DR: A class of the weighted edge corona product networks is defined, the generalized adjacency (resp., Laplacian and signless LaPLacian) spectra with two different structures are determined, and the number of spanning trees and Kirchhoff index of the weights are computed.
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Quantum transport on small-world networks: a continuous-time quantum walk approach.
TL;DR: The quantum mechanical transport of (coherent) excitons on small-world networks (SWNs) is very fast, given that the limiting value of the transition probability is reached very quickly, and that on average the exciton is most likely to be found at the initial node.
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Complete solution to a conjecture on the maximal energy of unicyclic graphs
TL;DR: It turns out that for n=4 the conjecture is not true, and P"4^3 should be the unicyclic graph with maximal energy.