Edge-removing games of star type Original Research Article

We define a new game, which is called an edge-removing game of star type. This game is played by two players on a graph G. Each player in turn removes a set of edges which induces a star, and the player who removes the last edge wins. This game is a generalization of the game of classical Nim and classical Kayles since if we play this game on a graph consisting of stars or one consisting of paths, then this game is equivalent to the game of classical Nim or classical Kayles. We give some results on this game.