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arXiv · 0806.0701

Number of connected spanning subgraphs on the Sierpinski gasket

Shu-Chiuan Chang·Lung-Chi Chen
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Abstract

We study the number of connected spanning subgraphs $f_{d,b}(n)$ on the generalized Sierpinski gasket $SG_{d,b}(n)$ at stage $n$ with dimension $d$ equal to two, three and four for $b=2$, and layer $b$ equal to three and four for $d=2$. The upper and lower bounds for the asymptotic growth constant, defined as $z_{SG_{d,b}}=\lim_{v \to \infty} \ln f_{d,b}(n)/v$ where $v$ is the number of vertices, on $SG_{2,b}(n)$ with $b=2,3,4$ are derived in terms of the results at a certain stage. The numerical values of $z_{SG_{d,b}}$ are obtained.

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Shu-Chiuan Chang, Lung-Chi Chen. 2008-06-04. Number of connected spanning subgraphs on the Sierpinski gasket. https://arxiv.org/abs/0806.0701

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