1 research outputs found
Pebble Exchange Group of Graphs
A graph puzzle of a graph is defined as follows. A
configuration of is a bijection from the set of vertices of a
board graph to the set of vertices of a pebble graph, both graphs being
isomorphic to some input graph . A move of pebbles is defined as exchanging
two pebbles which are adjacent on both a board graph and a pebble graph. For a
pair of configurations and , we say that is equivalent to if
can be transformed into by a finite sequence of moves.
Let be the automorphism group of , and let be
the unit element of . The pebble exchange group of , denoted
by , is defined as the set of all automorphisms of such
that and are equivalent to each other.
In this paper, some basic properties of are studied. Among
other results, it is shown that for any connected graph , all automorphisms
of are contained in , where is a square graph of .Comment: Accepted in European Journal of Combinatoric