Domination number of Token Graphs

The $k$-token graph of $G$ is the graph, $F_k(G)$, whose vertices are all the $k$-subsets of $V(G)$; with two of them adjacent whenever their symmetric difference is a pair of adjacent vertices in $G$. In this paper, we study the domination number of the token graphs of the star, $S_n$, and the complete graph, $K_n$.