November 8, 2025Open Access

A New Dominating Set Game on Graphs

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Winning strategies for dominating set games vary by graph types, including paths and cycles.
The last player choosing a vertex wins the dominating set game, particularly noted in structured graphs.
Combining graphs using Cartesian products and graph joins helps identify winning scenarios for the second player.
Insights on abelian groups indicate the second player wins when using canonical generating sets with even orders.

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Game analysis reveals winning strategies for the first player on paths and cycles, suggesting insights for various graph types.

Fiscus et al. (2025) studied this question.

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