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June 2016 Topological Symmetry Groups of Complete Bipartite Graphs
Kathleen HAKE, Blake MELLOR, Matt PITTLUCK
Tokyo J. Math. 39(1): 133-156 (June 2016). DOI: 10.3836/tjm/1459367261

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 $A_4$, $S_4$ or $A_5$ [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 $(\Z_r \x \Z_s) \ltimes \Z_2$.

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Kathleen HAKE. Blake MELLOR. Matt PITTLUCK. "Topological Symmetry Groups of Complete Bipartite Graphs." Tokyo J. Math. 39 (1) 133 - 156, June 2016. https://doi.org/10.3836/tjm/1459367261

Information

Published: June 2016
First available in Project Euclid: 30 March 2016

zbMATH: 1357.57012
MathSciNet: MR3543135
Digital Object Identifier: 10.3836/tjm/1459367261

Subjects:
Primary: 57M25
Secondary: 05C10

Rights: Copyright © 2016 Publication Committee for the Tokyo Journal of Mathematics

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Vol.39 • No. 1 • June 2016
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