The dynamics of several games on line graphs is studied. Relations between these games and a one-dimensional version of the sand pile model are established. We also study a generalization of the latter model, which we call the ice pile model. Specifically, we investigate the dynamical behavior of all these games and provide closed formulas for the transient time lengths they require to reach the steady state. © 1993.
Goles, E., & Kiwi, M. A. (1993). Games on line graphs and sand piles. Theoretical Computer Science, 115(2), 321–349. https://doi.org/10.1016/0304-3975(93)90122-A