The M-polynomial of Schreier Graphs of the Basilica and Grigorchuk Groups: Comparative Evaluation

A focus for comprehending the complex structures present in self-similar groups has been the study of Schreier graphs related to the Basilica and Grigorchuk group in recent years. Basic to group theory, Schreier graphs give a geometric picture of these groups’ actions on sets and shed light on the connectivity and symmetry characteristics of these groups. This paper examines the M-polynomial of Schreier graphs of the Basilica and Grigorchuk groups, examining its consequences for topological indices and comparing the determined values.