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  and independently Alon and Milman  states that .
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.
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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.
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Spectra of Graphs
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