Notes on the combinatorial game: Graph Nim

Richard M. LOW, Wai Hong CHAN

Research output: Contribution to journalArticlespeer-review

1 Citation (Scopus)


The combinatorial game of Nim can be played on graphs. Over the years, various Nim-like games on graphs have been proposed and studied by N.J. Calkin et al., L.A. Erickson and M. Fukuyama. In this paper, we focus on the version of Nim played on graphs which was introduced by N.J. Calkin et al.: Two players alternate turns, each time choosing a vertex v of a finite graph and removing any number (≥ 1) of edges incident to v. The player who cannot make a move loses the game. Here, we analyze Graph Nim for various classes of graphs and also compute some Grundy-values. Copyright © 2016 Bandung Indonesian Combinatorial Society.
Original languageEnglish
Pages (from-to)190-205
JournalElectronic Journal of Graph Theory and Applications
Issue number2
Publication statusPublished - 2016


Low, R. M., Chan, W. H. (2016). Notes on the combinatorial game: Graph Nim. Electronic Journal of Graph Theory and Applications, 4(2), 190-205.


  • Nim on graphs
  • Combinatorial game


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