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 root 3(2 root 3)(3n-1)/3 x (5(2)x7(2)x17(2)x/2(12)x3(5)x13)(16)(n). We also obtain the number of Hamiltonian walks with one end at a specific outmost vertex of SG(n), with asymptotic behavior root 3(2 root 3)(3n-1)/3 x (7x17/2(4)x3(3))4(n). 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. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3545358]