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.
Categories: math-ph math.MP