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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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A survey of results on integral trees and integral graphs
TL;DR: A graph is called integral if all zeros of the characteristic polynomial $P(G,x)$ are integers as mentioned in this paper, and a graph $G$ is called an integral graph if all the zeros are integers.
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Coxeter energy of graphs
Andrzej Mróz,Andrzej Mróz +1 more
TL;DR: In this article, the Coxeter energy of trees has been studied, and it has been shown that the path of the maximal star has the smallest (resp. the greatest) Coxeter Energy among all trees with fixed number of vertices.
Proceedings ArticleDOI
A Notion of Harmonic Clustering in Simplicial Complexes
Stefania Ebli,Gard Spreemann +1 more
TL;DR: In this article, a clustering scheme for simplicial complexes that produces clusters of simplices in a way that is sensitive to the homology of the complex is presented, which can be seen as a higher-dimensional version of graph spectral clustering.
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How much random a random network is : a random matrix analysis
TL;DR: In this paper, the authors analyzed complex networks under random matrix theory framework and showed that the long range correlations among eigenvalues provide a qualitative measure of randomness in networks, and that as networks deviate from the regular structure, $\Delta_3$ follows random matrix prediction of linear behavior, in semi-logarithmic scale with the slope of $1/pi^2.
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The Cycle-Path Indicator Polynomial of a Digraph
TL;DR: The cycle-path indicator polynomial of D can be obtained by a deletion?contraction recurrence relation of the digraph D and is considered as an application of chromatic arrangements of non-attacking rooks and the associatedPolynomial which is symmetric and generalizes the usual rook poynomial.