Enumeration of spanning trees in the sequence of Dürer graphs

Abstract

Abstract:In this paper, we calculate the number of spanning trees in the sequence of Dürer graphs with a special feature that it has two alternate states. Using the electrically equivalent transformations, we obtain the weights of corresponding equivalent graphs and further derive relationships for spanning trees between the Dürer graphs and transformed graphs. By algebraic calculations, we obtain a closed-form formula for the number of spanning trees with regard to iteration step. Finally we compare the entropy of our graph with other studied graphs and see that its value of entropy lies in the interval of those of graphs with average degree being 3 and 4.