Number of connected spanning subgraphs on the Sierpinski gasket

Shu-Chiuan Chang; Lung Chi Chen

Number of connected spanning subgraphs on the Sierpinski gasket

Shu-Chiuan Chang, Lung Chi Chen

Department of Physics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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→∞ 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.

Original language	English
Pages (from-to)	55-78
Number of pages	24
Journal	Discrete Mathematics and Theoretical Computer Science
Volume	11
Issue number	1
Publication status	Published - 2009 Jul 27

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)
Discrete Mathematics and Combinatorics

Cite this

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N2 - We study the number of connected spanning subgraphs fd,b(n) on the generalized Sierpinski gasket SGd,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 = limv→∞ ln f d,b(n)/v where v is the number of vertices, on SG2,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.

AB - We study the number of connected spanning subgraphs fd,b(n) on the generalized Sierpinski gasket SGd,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 = limv→∞ ln f d,b(n)/v where v is the number of vertices, on SG2,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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Number of connected spanning subgraphs on the Sierpinski gasket

Abstract

All Science Journal Classification (ASJC) codes

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