In this paper we complete the classification of topological symmetry groups
for complete graphs Knβ by characterizing which Knβ can have a cyclic
group, a dihedral group, or a subgroup of DmβΓDmβ where m is odd, as
its topological symmetry group.Comment: 19 pages; v2 lists authors correctly on arXiv; v3 substantially
revises the introductio