Arc Kayles is a combinatorial game played on a graph. We give nim-sequences for Arc Kayles on varying classes of graphs including: equimatchable graphs, path graphs, cycle graphs, and wheel graphs. Lastly, we provide an automatic periodicity check for generalized star graphs with three rays (two fixed) and conjecture about the period for generalized star graphs with one ray fixed to two vertices, a second ray fixed to n vertices (in an equivalence class modulo 34) and the third ray varying to infinity.
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