Faculty interested in undergraduate research
Darren Parker
Contact information: [email protected]
Office: MAK A-2-150
Research areas: Graph Theory and Games
Current projects: The Lights Out Game on Graphs
The original Lights Out game was a hand-held electronic game by Tiger Electronics. You begin with a 5x5 grid of buttons with lights in them. When the game is first turned on, some of those lights are on, and the others are off. The game is played by pushing the buttons. When a button is pushed, both the button pushed and each of its neighbors above, below, and to the side change their states from off to on or vice versa. The object of the game is to turn all the lights off. This game has been generalized to graphs in several ways, including allowing the lights not only to be “off” or “on”, but also to have different colors. Most recently, my students and I have been working on a directed graph version of the game. As in all versions of the game, it is possible to set up the directed graph, the initial colors, and the number of colors so that it is impossible to win the game. We look to prove theorems about when rigging the game is impossible.
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