Volume 6, Number 1, 2016, Pages 6575 DOI：10.11948/2016006 
Counting spanning trees in prism and antiprism graphs 
Weigang Sun,Shuai Wang,Jingyuan Zhang 
Keywords:Electrically equivalent transformation; spanning trees; prism graph; antiprism graph. 
Abstract: 
In this paper, we calculate the number of spanning trees in prism and antiprism graphs corresponding to the skeleton of a prism and an antiprism. By the electrically equivalent transformations and rules of weighted generating function, we obtain a relationship for the weighted number of spanning trees at the successive two generations. Using the knowledge of difference equations, we derive the analytical expressions for enumeration of spanning trees. In addition, we again calculate the number of spanning trees in Apollonian networks, which shows that this method is simple and effective. Finally we compare the entropy of our networks with other studied networks and find that the entropy of the antiprism graph is larger. 
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