Pebble exchange on graphs

@article{Fujita2015PebbleEO,
  title={Pebble exchange on graphs},
  author={Shinya Fujita and Tomoki Nakamigawa and Tadashi Sakuma},
  journal={Discrete Applied Mathematics},
  year={2015},
  volume={184},
  pages={139-145}
}
Let G and H be graphs with the same number of vertices. We introduce a graph puzzle ( G , H ) in which G is a board graph and the set of vertices of H is the set of pebbles. A configuration of H on G is defined as a bijection from the set of vertices of G to that of H . A move of pebbles is defined as exchanging two pebbles which are adjacent on both G and H . For a pair of configurations f and g , we say that g is equivalent to f if f can be transformed into g by a sequence of finite moves. If… CONTINUE READING

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