The Complexity of Classes of Pyramid Graphs Based on the Fritsch Graph and Its Related Graphs

A quantitative study of the complicated three-dimensional structures of artificial atoms in the field of intense matter physics requires a collaborative method that combines a statistical analysis of unusual graph features related to atom topology. Simplified circuits can also be produced by using similar transformations to streamline complex circuits that need laborious mathematical calculations during analysis. These modifications can also be used to determine the number of spanning trees required for specific graph families. The explicit derivation of formulas to determine the number of spanning trees for novel pyramid graph types based on the Fritsch graph, which is one of only six graphs in which every neighborhood is a 4- or 5-vertex cycle, is the focus of our study. We conduct this by utilizing our understanding of difference equations, weighted generating function rules, and the strength of analogous transformations found in electrical circuits.