caa a22 4500 445855762 CHVBK 20180317145427.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00026-011-0100-y doi (NATIONALLICENCE)springer-10.1007/s00026-011-0100-y The Number of Spanning Trees in Self-Similar Graphs [Elektronische Daten] [Elmar Teufl, Stephan Wagner] The number of spanning trees of a graph, also known as the complexity, is computed for graphs constructed by a replacement procedure yielding a self-similar structure. It is shown that under certain symmetry conditions exact formulas for the complexity can be given. These formulas indicate interesting connections to the theory of electrical networks. Examples include the well-known Sierpiński graphs and their higher-dimensional analogues. Several auxiliary results are provided on the way—for instance, a property of the number of rooted spanning forests is proven for graphs with a high degree of symmetry. Springer Basel AG, 2011 spanning trees nationallicence self-similar graphs nationallicence Teufl Elmar Fachbereich Mathematik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany aut Wagner Stephan Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, 7602, Matieland, South Africa aut Annals of Combinatorics SP Birkhäuser Verlag Basel 15/2(2011-06-01), 355-380 0218-0006 15:2<355 2011 15 26 https://doi.org/10.1007/s00026-011-0100-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00026-011-0100-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Teufl Elmar Fachbereich Mathematik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany aut NATIONALLICENCE 700 1- Wagner Stephan Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, 7602, Matieland, South Africa aut NATIONALLICENCE 773 0- Annals of Combinatorics SP Birkhäuser Verlag Basel 15/2(2011-06-01), 355-380 0218-0006 15:2<355 2011 15 26 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer