Enumeration of multivariate independence polynomial for iterations of Sierpinski triangle graph

Abstract

In dynamical systems, fractals and their features have been proven for a wide range of applications in graphical structures. In particular, self-similar graphs as well as graph polynomials play a vital role. This paper explores the characteristics of the polynomials for the family of well-known self-similar graphs, namely Sierpinski triangle graph of the \(n^{\text {th}}\) iteration, and proposes an algorithm to compute the multivariate independence polynomials of these graphs. We employ iterative patterns from the Sierpinski triangle graph, and we implement our approach to explicitly compute the independent sets to formulate multivariate independence polynomials for iterative values of n. In addition, the inverse of these polynomials have been computed using SAGE software.