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A FORMULA FOR THE NUMBER OF SPANNING TREES IN CIRCULANT GRAPHS WITH NONFIXED GENERATORS AND DISCRETE TORI

Part of: Graph theory

Published online by Cambridge University Press:  25 August 2015

JUSTINE LOUIS
JUSTINE LOUIS*
Affiliation:
Section of Mathematics, Université de Genève, 1211 Genève 4, Switzerland email justine.louis@unige.ch
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Abstract

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We consider the number of spanning trees in circulant graphs of ${\it\beta}n$ vertices with generators depending linearly on $n$. The matrix tree theorem gives a closed formula of ${\it\beta}n$ factors, while we derive a formula of ${\it\beta}-1$ factors. We also derive a formula for the number of spanning trees in discrete tori. Finally, we compare the spanning tree entropy of circulant graphs with fixed and nonfixed generators.

Keywords

spanning treescirculant graphsspanning tree entropy

MSC classification

Primary: 05C05: Trees
Secondary: 05C30: Enumeration in graph theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 3 , December 2015 , pp. 365 - 373
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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