Number of connected spanning subgraphs on the Sierpinski gasket

Details Number of connected spanning subgraphs on the Sierpinski gasket Number of connected spanning subgraphs on the Sierpinski gasket

2008-06-04

arxiv.org/abs/0806.0701v1

Physics

Mathematical Physics

25 pages, 8 figures, 9 tables

Scientific paper

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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