Classification of topological symmetry groups of $K_n$
  In this paper we complete the classification of topological symmetry groups for complete graphs $K_n$ by characterizing which $K_n$ can have a cyclic group, a dihedral group, or a subgroup of $D_m \times D_m$ where $m$ is odd, as its topological symmetry group. 
Erica Flapan, Blake Mellor, Ramin Naimi and Michael Yoshizawa
math.GT math.CO