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

*Shu-Chiuan Chang, Lung-Chi Chen*

#### 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_{SGd,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_{SGd,b}are obtained.Full Text: PDF PostScript