Algorithms for Chip-Firing on Weighted Graphs

Ben Doyle

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arXiv · 2311.00194

Algorithms for Chip-Firing on Weighted Graphs

Ben Doyle

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Abstract

We extend the notion of chip-firing to weighted graphs, and generalize the Greedy Algorithm and Dhar's Burning Algorithm to weighted graphs. For a vertex $q \in V(Γ)$, we give an upper bound for the number of linearly equivalent $q$-reduced divisors. Finally, we illustrate a method of finding all maximal unwinnable divisors on weighted graphs.

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Ben Doyle. 2023-10-31. Algorithms for Chip-Firing on Weighted Graphs. https://arxiv.org/abs/2311.00194

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