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As a classic self-similar network model, Sierpinski gasket network has beenused many times to study the characteristics of self-similar structure and itsinfluence on the dynamic properties of the network. However, the network modelsstudied in these problems only contain a single self-similar structure, whichis inconsistent with the structural characteristics of the actual networkmodels. In this paper, a type of horizontally segmented 3 dimensionalSierpinski gasket network is constructed, whose main feature is that itcontains the locally self-similar structures of the 2 dimensional Sierpinskigasket network and the 3 dimensional Sierpinski gasket network at the sametime, and the scale transformation between the two kinds of self-similarstructures can be controlled by adjusting the crosscutting coefficient. Theanalytical expression of the average trapping time on the network model issolved, which used to analyze the effect of two types of self-similarstructures on the properties of random walks. Finally, we conclude that thedominant self-similar structure will exert a greater influence on the randomwalk process on the network.

Average trapping time on a type of horizontally segmented 3 dimensional Sierpinski gasket network with two types of locally self-similar structures