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Spanning trees and recurrent configurations of a graph

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  • Wu, Xiaoxia
  • Zhang, Lianzhu
  • Chen, Haiyan

Abstract

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.

Suggested Citation

  • Wu, Xiaoxia & Zhang, Lianzhu & Chen, Haiyan, 2017. "Spanning trees and recurrent configurations of a graph," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 25-30.
    • Handle: RePEc:eee:apmaco:v:314:y:2017:i:c:p:25-30
    DOI: 10.1016/j.amc.2017.06.030
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    References listed on IDEAS

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    1. Majumdar, S.N. & Dhar, Deepak, 1992. "Equivalence between the Abelian sandpile model and the q→0 limit of the Potts model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 129-145.
    2. Chen, Ailian & Xiong, Xianzhu & Lin, Fenggen, 2016. "Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1100-1106.
    3. Dhar, Deepak, 2006. "Theoretical studies of self-organized criticality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(1), pages 29-70.
    4. Gutman, Ivan, 2016. "On Steiner degree distance of trees," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 163-167.
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