Counting Spanning Trees in The Ladders

Abstract

Aims: In order to study the rule of entropy in different graph transformations, this paper introduces and further generalizes the ladder graph from different perspectives, including pinwheel ladders and 3-dimensional ladders. Then the problem of entropy comes down to the calculation of spanning trees in these graphs. Place and Duration of Study: School of Mathematical Sciences, Jiangsu University, between January 2023 and October 2023. Methodology: A method by seeking similar terms was generalized to help study the essential principle in these graphs. By similarity diagonalization and computer aided calculation, the exact expressions for the number of spanning trees in these graphs are obtained.