https://doi.org/10.1140/epjs/s11734-024-01304-1
Regular Article
Enumeration of multivariate independence polynomial for iterations of Sierpinski triangle graph
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India
Received:
4
April
2024
Accepted:
7
August
2024
Published online:
26
August
2024
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 
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.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
