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Number of connected spanning subgraphs on the Sierpinski gasket

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 zSG(d,b) = lim(v ->infinity) 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.
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Shu-Chiuan Chang, Lung-Chi Chen. Number of connected spanning subgraphs on the Sierpinski gasket. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2009, Vol. 11 no. 1 (1), pp.55--77. ⟨10.46298/dmtcs.470⟩. ⟨hal-00988182⟩



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