Graph Nim

Nim is a well-known two-player impartial combinatorial game. Various versions of playing Nim on graphs have been investigated. We investigate a new version of Nim called Graph Nim. Given a graph with n vertices and multiple edges, players take turns removing edges until there are no edges left. Players have to choose a vertex and remove at least one edge incident to the chosen vertex. The player that removes the last edge or edges wins the game. In this paper, we give the solution for certain game boards of Graph Nim, compare the game of Graph Nim to another impartial combinatorial game, and discuss open problems