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The orientation preserving topological symmetry group of a graph embedded in the 3-sphere is the subgroup of the automorphism group of the graph consisting of those automorphisms which can be induced by an orientation preserving homeomorphism of the ambient space. We characterize all possible orientation preserving topological symmetry groups of embeddings… (More)

Site-specific recombination on supercoiled circular DNA yields a variety of knotted or catenated products. Here, we present a topological model of this process and characterize all possible products of the most common substrates: unknots, unlinks, and torus knots and catenanes. This model tightly prescribes the knot or catenane type of previously… (More)

We prove that for every closed, connected, orientable, irre-ducible 3-manifold, there exists an alternating group An which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group G, there is an embedding Γ of some graph in a hyperbolic rational homology 3-sphere such that the topological symmetry… (More)

- Erica Flapan, Thomas W Mattman, Blake Mellor, Ramin Naimi
- 2016

This article presents a survey of some recent results in the theory of spatial graphs. In particular, we highlight results related to intrinsic knotting and linking and results about symmetries of spatial graphs. In both cases we consider spatial graphs in S 3 as well as in other 3-manifolds.

We characterize which 3-connected graphs are intrinsically chiral in terms of whether or not a certain type of graph automorphism exists. 1996 Academic Press, Inc. Recently, topology and graph theory have come together to study graphs embedded in 3-space, (see for example [115]). An analysis of the symmetries of spatial graphs is useful in chemistry in… (More)

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