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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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Journal ArticleDOI
Interlacing eigenvalues and graphs
TL;DR: In this paper, bounds are obtained for characteristic numbers of graphs, such as the size of a maximal clique, the chromatic number, the diameter, and the bandwidth, in terms of the eigenvalues of the standard adjacency matrix or the Laplacian matrix.
Proceedings ArticleDOI
Spectral K-Way Ratio-Cut Partitioning and Clustering
TL;DR: A spectral approach to multiway ratio-cut partitioning is developed which provides a generalization of the ratio- cut cost metric to k-way partitioning and a lower bound on this cost metric.
Book ChapterDOI
Diffusion adaptation over networks
TL;DR: Adaptive networks are well suited to perform decentralized information processing and optimization tasks and to model various types of self-organized and complex behavior encountered in nature as discussed by the authors, where agents are linked together through a connection topology, and they cooperate with each other through local interactions to solve distributed optimization, estimation, and inference problems in real-time.
Journal ArticleDOI
On some counting polynomials in chemistry
TL;DR: Various counting polynomials suggested by chemical and physical problems are discussed and Mathematical relations among them and physico-chemical interpretations are given.
Journal ArticleDOI
Spectra of uniform hypergraphs
Joshua Cooper,Aaron Dutle +1 more
TL;DR: In this paper, a spectral theory of uniform hypergraphs is presented, which closely parallels Spectral Graph Theory (SG Theory), and a number of natural analogies of basic results in SG Theory are established.