Independence polynomial of the Sierpinski gasket graph and the tower of Hanoi graph

Abstract

In dynamical systems, the most well-known fractals are the Sierpinski gasket graph, also known as the Sierpinski fractal, and the Tower of Hanoi graph. In this paper, we investigate the n^th generated independence polynomial of these graphs as well as its properties. In order to partition its spanning subgraphs, we use iterative patterns of the Sierpinski graph and the Hanoi graph. Furthermore, we consider the relationship between the Tower of Hanoi graph and the Sierpinski fractal in terms of their independence polynomial.