Hamiltonian walks on the Sierpinski gasket

We derive the exact number of Hamiltonian walks H(n) on the two-dimensional Sierpinski gasket SG(n) at stage n, whose asymptotic behavior is given by. We also obtain the number of Hamiltonian walks with one end at a specific outmost vertex of SG(n), with asymptotic behavior. The distribution of Hamiltonian walks on SG(n) with one end at a specific outmost vertex and the other at an arbitrary vertex of SG(n) is investigated. We rigorously prove that the exponent for the mean l displacement between the two end vertices of such Hamiltonian walks on SG(n) is l ln 2/ln 3 for l > 0.