Average trapping time on horizontally divided 3-dimensional 3-level Sierpinski gasket network

Abstract

An important characteristic of random wandering is the average trapping time, which is a hot issue in current research. The average trapping time is an important measure of the transmission efficiency of random wandering in a network. In this paper, we construct a 3-dimensional 3-level Sierpinski gasket network divided horizontally by the horizontal division plane Ps, that is, the division coefficients s.
We study the capture problem on the network and obtain an analytical expression for the average trapping time(ATT). Then, by adjusting the number of iterations and the values of the division coefficients, we obtained the relationship between ATT and
them. As can be seen from the plotted Fig. 7, ATT is affected by s. The larger s is, the more the self-similar structure of the three-dimensional residual network gradually transforms towards the structure of the two-dimensional complete Sierpinski gasket network. Meanwhile, the shorter ATT is,that is, the more efficient the transmission on the network.