Peg solitaire game on Sierpinski graphs

Abstract

The peg solitaire game is generalized to arbitrary boards by Beeler and Hoilman. These boards are considered as connected graphs in the combinatorial sense. In this study, peg solitaire game on Sierpinski graphs is considered, and it is proved that Sierpinski graphs are freely solvable, it means that, it can be solved from any starting position. Furthermore, we prove that the final peg can be left in any vertex.

Subject Classification: (2010):

• 91A46
• 05C57

Keywords:

• Sierpinski graph
• Peg solitaire game
• Games on graphs