Hitting time for random walks on the Sierpinski network and the half Sierpinski network

We consider the unbiased random walk on the Sierpinski network (S n ◦N) and the half Sierpinski network (HS n ◦N), where n is the generation. Different from the existing works on the Sierpinski gasket, S n ◦N is generated by the nested method and HS n ◦N is half of S n ◦N based on the vertical cutting of the symmetry axis. We study the hitting time on S n ◦N and HS n ◦N. According to the complete symmetry and structural properties of S n ◦N, we derive the exact expressions of the hitting time on the nth generation of S n ◦N and HS n ◦N. The curves of the hitting time for the two networks are almost consistent when n is large enough. The result indicates that the diffusion efficiency of HS n ◦N has not changed greatly compared with S n ◦N at a large scale.