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math.CO2025
Periods and atomic firing sequences of parallel chip-firing games on directed graphs
David Ji, Michael Li, Daniel Wang
In 1992, Bitar and Goles introduced the parallel chip-firing game on undirected graphs. Two years later, Prisner extended the game to directed graphs. While the properties of paral…
math.CO2024
Non-Stabilizing Parallel Chip-Firing Games
David Ji, Michael Li, Daniel Wang
In 2010, Kominers and Kominers proved that any parallel chip-firing game on with chips stabilizes. Recently, Bu, Choi, and Xu made the bound exact: a…
math.CO2024
Increasingly Many Bounded Eigenvalues of the Graph of Whitehead Moves
Michael Li
In this paper, we investigate the eigenvalues of the Laplacian matrix of the "graph of graphs", in which cubic graphs of order n are joined together using Whitehead moves. Our work…