A Variation on Chip-Firing: the diffusion game
| Autor: | Duffy, C., Lidbetter, T. F., Messinger, M. E., Nowakowski, R. J. |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Discrete Mathematics & Theoretical Computer Science, Vol. 20 no. 1, Graph Theory (January 17, 2018) dmtcs:2039 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.23638/DMTCS-20-1-4 |
| Popis: | We introduce a natural variant of the parallel chip-firing game, called the diffusion game. Chips are initially assigned to vertices of a graph. At every step, all vertices simultaneously send one chip to each neighbour with fewer chips. As the dynamics of the parallel chip-firing game occur on a finite set the process is inherently periodic. However the diffusion game is not obviously periodic: even if $2|E(G)|$ chips are assigned to vertices of graph G, there may exist time steps where some vertices have a negative number of chips. We investigate the process, prove periodicity for a number of graph classes, and pose some questions for future research. Comment: 18 pages, 3 figures |
| Databáze: | arXiv |
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