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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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Estrada Index of Random Graphs
Zhi Chen,Yi-Zheng Fan +1 more
TL;DR: In this article, the Estrada index of a graph G of order n is defined as EE(G )= � n=1 e λ i, where λ 1,λ 2,...,λ n are the eigenvalues of the graph G. By the limiting behavior of the spectrum of random symmetric matrices, the authors formulate an exact estimate to EE (G )f or almost all graphs G, and establish a lower bound and an upper bound for almost all multipartite graphs G.
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The Estrada index of trees
Zhibin Du,Bo Zhou +1 more
TL;DR: Li et al. as discussed by the authors gave a proof of a conjecture on trees with minimum Estrada index among the set of trees with two adjacent vertices of maximum degree, and then they determined the unique tree with maximum EStrada index with given number of pendant vertices.
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About small eigenvalues of the Witten Laplacian
TL;DR: In this article, the low-lying eigenvalues of the Witten Laplacian associated to a Morse function φ were studied and general distributions of critical values of φ, for instance allowing all the local minima to be absolute.
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Complete spectrum of stochastic master equation for random walks on treelike fractals
TL;DR: In this paper, the authors studied random walks on a family of treelike regular fractals with a trap fixed on a central node and obtained all the eigenvalues and their corresponding multiplicities for the associated stochastic master equation.
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On the estrada index of graphs with given number of cut edges.
Zhibin Du,Bo Zhou +1 more
TL;DR: In this article, the unique graph with maximum Estrada index is determined among connected graphs with given numbers of vertices and cut edges, and the EstrADA index of G is defined as EE(G) = ∑ n i = 1 ei.