Spectra of Graphs


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In most recent years, the spectral graph theory has expanded to vertex-varying graphs often encountered in many real-life applications. From Wikipedia, the free encyclopedia. Main article: Cheeger constant graph theory. Hamburg 21, 63—77, Smallest pair of isospectral polyhedral graphs with eight vertices", Journal of Chemical Information and Modeling , 34 2 : —, doi : Harary, Ed. Christopher David Meagher, Karen College teacher.

Cambridge, United Kingdom. Recent Results in the Theory of Graph Spectra. Annals of Discrete mathematics. Applied and Computational Harmonic Analysis. Categories : Algebraic graph theory Spectral theory. The Cheeger constant as a measure of "bottleneckedness" is of great interest in many areas: for example, constructing well-connected networks of computers , card shuffling , and low-dimensional topology in particular, the study of hyperbolic 3- manifolds. More formally, the Cheeger constant h G of a graph G on n vertices is defined as.

An inequality due to Dodziuk [9] and independently Alon and Milman [10] states that [11].

Spectra of Graphs Universitext

This inequality is closely related to the Cheeger bound for Markov chains and can be seen as a discrete version of Cheeger's inequality in Riemannian geometry. There is an eigenvalue bound for independent sets in regular graphs , originally due to Alan J. Hoffman and Philippe Delsarte. This bound has been applied to establish e.

Spectra of graphs and applications

Spectral graph theory emerged in the s and s. Besides graph theoretic research on the relationship between structural and spectral properties of graphs, another major source was research in quantum chemistry , but the connections between these two lines of work were not discovered until much later. In most recent years, the spectral graph theory has expanded to vertex-varying graphs often encountered in many real-life applications. From Wikipedia, the free encyclopedia.

Main article: Cheeger constant graph theory.

Submission history

Hamburg 21, 63—77, Miao, Spectra of the subdivision-vertex and subdivision-edge coronae, arXiv preprint arXiv McLeman and E. Merris, Laplacian matrices of graphs: a survey, Linear algebra and its applications, , pp. Merris, Laplacian graph eigenvectors, Linear algebra and its applications, , pp. Mohar, Laplacian eigenvalues of graphs - a survey, Discrete Mathematics, , pp. Mohar, The Laplacian spectrum of graphs, Graph theory, combinatorics, and applications, 2 , pp.

Shinoda, On the characteristic polynomial of the adjacency matrix of the subdivision graph of a graph, Discrete Applied Mathematics, 2 , pp. Tavakoli, F. Rahbarnia and A.


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Ashra, Note on strong product of graphs, Kragujevac Journal ofMathematics, 37 , pp. Wang and B. Zhou, The signless Laplacian spectra of the corona and edge corona of two graphs, Linear and Multilinear Algebra, 61 , pp.

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Wu, Y. Lou and C. Xu and C. He, On the signless Laplacian spectral determination of the join of regular graphs, Discrete Mathematics, Algorithms and Applications, 6 , pp. Export Citation. Barik et al. User Account Log in Register Help.


  • Spectra of Graphs!
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Search Close Advanced Search Help. Show Summary Details. More options …. Special Matrices. Editor-in-Chief: da Fonseca, Carlos Martins. Open Access. Online ISSN See all formats and pricing Online.

Spectra of R-Vertex Join and R-Edge Join of Two Graphs

Prices are subject to change without notice. Prices do not include postage and handling if applicable. Navid and Salehy, S. Nima Sylvester Hadamard matrices revisited by Mitrouli, M.

Spectra of Graphs

A note on the determinant of a Toeplitz-Hessenberg matrix by Merca, Mircea The theory and applications of complex matrix scalings by Pereira, Rajesh and Boneng, Joanna Moore-Penrose inverse of a hollow symmetric matrix and a predistance matrix by Kurata, Hiroshi and Bapat, Ravindra B. On characteristic and permanent polynomials of a matrix by Singh, Ranveer and Bapat, R.

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Farewell, pairing? An approach based on matrix polynomials for linear systems of partial differential equations by Shayanfar, N.

Volume 6 Issue 1 Jan , pp. Volume 5 Issue 1 Jan , pp. Volume 4 Issue 1 Jan Volume 3 Issue 1 Jan Volume 2 Issue 1 Jan Volume 1 Issue Jan , pp.

Spectra of Graphs Spectra of Graphs
Spectra of Graphs Spectra of Graphs
Spectra of Graphs Spectra of Graphs
Spectra of Graphs Spectra of Graphs
Spectra of Graphs Spectra of Graphs
Spectra of Graphs Spectra of Graphs
Spectra of Graphs Spectra of Graphs

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