Number of connected spanning subgraphs on the Sierpinski gasket

Abstract

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 zSGd,b=limv →∞ ln fd,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 zSGd,b are obtained.