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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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On the Estrada and Laplacian Estrada indices of graphs
Zhibin Du,Zhongzhu Liu +1 more
TL;DR: In this paper, the change of Laplacian Estrada index of bipartite graph under edge grafting operation between two pendent paths at the same vertex was studied.
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The relationship between the eccentric connectivity index and Zagreb indices
Hongbo Hua,Kinkar Ch. Das +1 more
TL;DR: This paper first gives some sufficient conditions for a graph G satisfying @x^c(G)@?M"i(G), i=1,2, and introduces two classes of composite graphs, each of which has larger eccentric connectivity index than the first Zagreb index.
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Lower bounds for Estrada index and Laplacian Estrada index
TL;DR: Some new lower bounds for EE and LEE are obtained and shown to be the best possible.
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Correlation length, isotropy and meta-stable states
TL;DR: The correlation length conjecture as mentioned in this paper allows to estimate the number of meta-stable states from the correlation length, provided the landscape is "typical", i.e., a landscape is rugged if it has many local optima, if it gives rise to short adaptive walks, and if it exhibits a rapidly decreasing pair correlation function.
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Spectral properties of complex networks
Camellia Sarkar,Sarika Jalan +1 more
TL;DR: This review presents an account of the major works done on spectra of adjacency matrices drawn on networks and the basic understanding attained so far, divided under three sections: extremal eigenvalues, bulk part of the spectrum, and degenerate eigen Values, based on the intrinsic properties of eigen values and the phenomena they capture.