Peg solitaire game on Sierpinski graphs
Handan Akyar, Nazlıcan Çakmak, Nilay Torun, Emrah Akyar · Journal of Discrete Mathematical Sciences and Cryptography · 2021
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.