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    Strichartz, Robert S. and Teplyaev, Alexander 2012. Spectral analysis on infinite Sierpiński fractafolds. Journal d'Analyse Mathématique, Vol. 116, Issue. 1, p. 255.


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COMB GRAPHS AND SPECTRAL DECIMATION

  • JONATHAN JORDAN (a1)
  • DOI: http://dx.doi.org/10.1017/S0017089508004540
  • Published online: 01 January 2009
Abstract
Abstract

We investigate the spectral properties of matrices associated with comb graphs. We show that the adjacency matrices and adjacency matrix Laplacians of the sequences of graphs show a spectral similarity relationship in the sense of work by L. Malozemov and A. Teplyaev (Self-similarity, operators and dynamics, Math. Phys. Anal. Geometry6 (2003), 201–218), and hence these sequences of graphs show a spectral decimation property similar to that of the Laplacians of the Sierpiński gasket graph and other fractal graphs.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1.L. Accardi , A. Ben Ghorbal and N. Obata , Monotone independence, comb graphs and Bose-Einstein condensation, Infin. Dimen. Anal. Quantum Probab. Relat. Top 7 (2004), 419435.

2.N. Bajorin , T. Chen , A. Dagan , C. Emmons , M. Hussein , M. Khalil , P. Mody , B. Steinhurst and A. Teplyaev , Vibration nodes of 3n-gaskets and other fractals, J. Phys. A 41 (015101), 2008.

4.F. Chung , L. Lu and V. Vu , Spectra of random graphs with given expected degrees, Proc. Nat. Acad. Sci. 100 (2003), 63136318.

5.F. R. K. Chung , Spectral graph theory (AMS, Providence, Rhode Island, 1997). Number 92 in CBMS Regional Conference Series.

6.M. Fukushima and T. Shima , On a spectral analysis for the Sierpiński gasket, Potential Anal. 1 (1992), 135.

8.L. Malozemov and A. Teplyaev , Self-similarity, operators and dynamics, Math. Phys. Anal. Geometry 6 (2003), 201218.

9.R. Rammal and G. Toulouse , Random walks on fractal structures and percolation clusters, J. Physique Letters 44 (1983), L13L22.

10.J. H. Schenker and M. Aizenman , The creation of spectral gaps by graph decoration, Lett. Math. Phys. 53 (2000), 253262.

11.T. Shima , On eigenvalue problems for the random walks on the Sierpiński pre-gaskets, Japan. J. Indust. Appl. Math. 8 (1991), 127141.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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