uu.seUppsala University Publications

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Counting spanning trees on fractal graphs and their asymptotic complexityPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2016 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 49, no 35, article id 355101Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2016. Vol. 49, no 35, article id 355101
##### Keywords [en]

fractal graphs, spanning trees, spectral decimation, asymptotic complexity
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-304155DOI: 10.1088/1751-8113/49/35/355101ISI: 000381302500005OAI: oai:DiVA.org:uu-304155DiVA, id: diva2:1014934
#####

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt449",{id:"formSmash:j_idt449",widgetVar:"widget_formSmash_j_idt449",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt455",{id:"formSmash:j_idt455",widgetVar:"widget_formSmash_j_idt455",multiple:true}); Available from: 2016-10-03 Created: 2016-10-03 Last updated: 2018-12-17Bibliographically approved
##### In thesis

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.

1. Combinatorial and analytical problems for fractals and their graph approximations$(function(){PrimeFaces.cw("OverlayPanel","overlay1271631",{id:"formSmash:j_idt733:0:j_idt737",widgetVar:"overlay1271631",target:"formSmash:j_idt733:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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