Enumerating the Number of Spanning Trees of Pyramid Graphs Based on Some Nonahedral Graphs

The enumeration of spanning trees in various graph forms has been made easier by the study of electrically equivalent transformations, which was motivated by Kirchhoff’s work on electrical networks. In this work, using knowledge of difference equations, the electrically equivalent transformations and rules of weighted generating function are used to calculate the explicit formulas of the number of spanning trees of novel pyramid graph types based on some nonahedral graphs. Lastly, we compare our graphs’ entropy with that of other average-degree graphs that have been researched.