Complexity and Entropy of Sequence of Some Families of Graphs Created by a Triangle that Have the Same Average Degree (Contemporary Mathematics, 2025)
In physics, complex circuits that need multiple mathematical operations to analyze can be reduced to simpler equivalent circuits using equivalent transformations. These modifications can also be used to find the number of spanning trees in specific graph families. In the current study, we calculate the explicit formulae for the number of spanning trees of sequences of new families of graphs formed by a triangle with the same average degree using our understanding of difference equations, electrically equivalent transformations, and weighted generating function rules. We conclude by comparing our graphs’ entropy to similar graphs with an average degree of four.
Keywords: number of spanning trees; electrically equivalent transformations; entropy