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Counting spanning trees on fractal graphs and their asymptotic complexity
Univ Illinois, Dept Math, Urbana, IL 61801 USA..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 49, no 35, 355101Article in journal (Refereed) Published
Abstract [en]

Using the method of spectral decimation and a modified version of Kirchhoff's matrix-tree theorem, a closed form solution to the number of spanning trees on approximating graphs to a fully symmetric self-similar structure on a finitely ramified fractal is given in theorem 3.4. We show how spectral decimation implies the existence of the asymptotic complexity constant and obtain some bounds for it. Examples calculated include the Sierpinski gasket, a non-post critically finite analog of the Sierpinski gasket, the Diamond fractal, and the hexagasket. For each example, the asymptotic complexity constant is found.

Place, publisher, year, edition, pages
2016. Vol. 49, no 35, 355101
Keyword [en]
fractal graphs, spanning trees, spectral decimation, asymptotic complexity
National Category
URN: urn:nbn:se:uu:diva-304155DOI: 10.1088/1751-8113/49/35/355101ISI: 000381302500005OAI: oai:DiVA.org:uu-304155DiVA: diva2:1014934
Available from: 2016-10-03 Created: 2016-10-03 Last updated: 2016-10-03Bibliographically approved

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Tsougkas, Konstantinos
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Analysis and Probability Theory
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