Abstract
Björner, Lovász and Shor introduced a chip-firing game on a finite graph \(G\) as follows. We put some chips on each vertex of \(G\), we say that a vertex is ready if it has at least as many chips as its degree, in which case we can fire it and the result is that it distributes one chip to each of its neighbors, this may cause other vertices to be ready, and so on. This game continues until no vertex can be fired. In this paper, we study chip-firing games on complete graphs. We obtain a sufficient and necessary condition for chip-firing games on complete graphs to be finite.
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Acknowledgments
The research is supported by NSFC (No. 11301371) and YKJ12026R. Weihua Yang is the corresponding author of the article.
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Communicated by Xueliang Li.
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Zhuang, W., Yang, W., Zhang, L. et al. Properties of Chip-Firing Games on Complete Graphs. Bull. Malays. Math. Sci. Soc. 38, 1463–1469 (2015). https://doi.org/10.1007/s40840-014-0101-1
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DOI: https://doi.org/10.1007/s40840-014-0101-1