Topological Symmetry Groups of Complete Bipartite Graphs

Authors

Kathleen Hake
Blake Mellor, Loyola Marymount UniversityFollow
Matthew Pittluck

Document Type

Article

Publication Date

6-2016

Abstract

The symmetries of complex molecular structures can be modeled by the {\em topological symmetry group} of the underlying embedded graph. It is therefore important to understand which topological symmetry groups can be realized by particular abstract graphs. This question has been answered for complete graphs [7]; it is natural next to consider complete bipartite graphs. In previous work we classified the complete bipartite graphs that can realize topological symmetry groups isomorphic to A₄ , S₄ or A₅ [12]; in this paper we determine which complete bipartite graphs have an embedding in S 3 whose topological symmetry group is isomorphic to \Z_m, D_m, \Z_r\x\Z_s or ( \Z_r\x \Z_s) ⋉ \Z₂.

Recommended Citation

Hake, Kathleen, Blake Mellor, and Matt Pittluck. “Topological Symmetry Groups of Complete Bipartite Graphs.” Tokyo Journal of Mathematics 39, no. 1 (June 2016): 133–56. https://doi.org/10.3836/tjm/1459367261.