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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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Efficiently spotting the starting points of an epidemic in a large graph
TL;DR: This paper gives an efficient method called NetSleuth, which gives an highly efficient algorithm to identify likely sets of seed nodes given a snapshot, and shows it can optimize the virus propagation ripple in a principled way by maximizing likelihood.
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Local and Nonlocal Discrete Regularization on Weighted Graphs for Image and Mesh Processing
TL;DR: A discrete regularization framework on weighted graphs of arbitrary topology, which unifies local and nonlocal processing of images, meshes, and more generally discrete data, and provides a discrete extension of these regularization methods for any discrete data or functions.
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Transportation in graphs and the admittance spectrum
TL;DR: Borders are given for the decrease of the second eigenvalue caused by the insertion of an edge into a graph and its corresponding eigenvectors.
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Skew-adjacency matrices of graphs
Michael S. Cavers,Sebastian M. Cioabă,Shaun M. Fallat,David A. Gregory,Willem H. Haemers,Steve Kirkland,Judith J. McDonald,Michael J. Tsatsomeros +7 more
TL;DR: In this paper, the spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs, and an analogue of the Perron-Frobenius theorem is proposed.
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Applications of a theorem by Ky Fan in the theory of graph energy
TL;DR: In this article, the Ky Fan theorem is applied to the theory of graph energy, resulting in several new inequalities, as well as new proofs of some earlier known inequalities, in the case of graph adjacency matrices.