Spanning Trees And Tree Entropy On The Sierpinski Gasket Type Graphs

In this thesis,we calculate the number of spanning trees for the Sierpinski gasket type graphs,and study the associated asymptotic complexity,call it the tree entropy.For a certain family of subsets contains in the Sierpinski gasket,we consider their associated graph approximations,and prove that the number of spanning trees grows exponentially with the number of vertices of the graphs,and the exponential ratio(tree entropy)remains the same for the family of subsets.Moreover,for each approxima-tion graphs,the number of spanning trees can be expressed asymptotically by the tree entropy,number of vertices,subentropy and number of boundary vertices.