Spanning trees and recurrent configurations of a graph

摘要

A new explicit relationship between spanning trees and recurrent configurations of a graph is given by constructing subtree. Applying this relationship, we determine the total number of topplings in an avalanche. As applications, we calculate the sizes of avalanches of the Abelian sandpile model on the complete graph, the wheel and the complete bipartite graph. (C) 2017 Published by Elsevier Inc.