Topological Symmetry Groups of the Heawood Graph
We classify all groups which can occur as the topological symmetry group of some embedding of the Heawood graph in $S^3$.
math.GT↗
arXiv subjects
Publications and source records attributed to Emille Davie Lawrence.
We classify all groups which can occur as the topological symmetry group of some embedding of the Heawood graph in $S^3$.
We give a description of the cycle structure of the Heawood graph, $C_{14}$. In particular, we prove that the automorphism group of $C_{14}$ acts transitively on the set of $12$-cycles, Hamiltonian cycles, and disjoint pairs of $6$-cycles. We also enumerate $12$-, $10$-, and $8$-cycles in $C_{14}$, as well as pairs of disjoint $6$-cycles.
We classify all groups which can occur as the orientation preserving topological symmetry group of some embedding of a Möbius ladder graph in $S^3$.