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 $S{G}_{d,b}(n)$ 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 $z_{S{G}_{d,b}}={\lim }_{v\to \infty }\ln f_{d,b}(n)/v$ where $v$ is the number of vertices, on $S{G}_{2,b}(n)$ with $b=2,3,4$ are derived in terms of the results at a certain stage. The numerical values of $z_{S{G}_{d,b}}$ are obtained.

25 pages, 8 figures, 9 tables

References in corpus (2)

• Spanning trees on the Sierpinski gasket
• Exact Potts Model Partition Functions on Wider Arbitrary-Length Strips of the Square Lattice