On the 2-token graph of a graph

Abstract Let G = ( V , E ) be a graph and let k be a positive integer. Let P k ( V ) = { S : S ⊆ V and | S | = k } . The k -token graph F k ( G ) is the graph with vertex set P k ( V ) and two vertices A and B are adjacent if A Δ B = { a , b } and a b ∈ E ( G ) , where Δ denotes the symmetric difference. In this paper we present several basic results on 2-token graphs.