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Number of connected spanning subgraphs on the Sierpiński gasket. (English) Zbl 1196.05040
Summary: 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 $$zSG_{d,b}=lim_{v \to \infty } \ln f_{d,b}(n)/v$$ 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 $$zSG_{d,b}$$ are obtained.

MSC:
 05C30 Enumeration in graph theory
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