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 n th 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.