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A FORMULA FOR THE NUMBER OF SPANNING TREES IN CIRCULANT GRAPHS WITH NONFIXED GENERATORS AND DISCRETE TORI
Published online by Cambridge University Press: 25 August 2015
Abstract
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.
- 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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