相关论文: Topological Symmetry Groups of Complete Bipartite …

We determine for which $n$, the complete bipartite graph $K_{n,n}$ has an embedding in $S^3$ whose topological symmetry group is isomorphic to one of the polyhedral groups: $A_4$, $A_5$, or $S_4$.

We determine for which $m$, the complete graph $K_m$ has an embedding in $S^3$ whose topological symmetry group is isomorphic to one of the polyhedral groups: $A_4$, $A_5$, or $S_4$.

The {\em topological symmetry group} of an embedding $\Gamma$ of an abstract graph $\gamma$ in $S^3$ is the group of automorphisms of $\gamma$ which can be realized by homeomorphisms of the pair $(S^3, \Gamma)$. These groups are motivated…

The {\em topological symmetry group} of an embedding $\Gamma$ of an abstract graph $\gamma$ in $S^3$ is the group of automorphisms of $\gamma$ which can be realized by homeomorphisms of the pair $(S^3, \Gamma)$. These groups are motivated…

We present the concept of the topological symmetry group as a way to analyze the symmetries of non-rigid molecules. Then we characterize all of the groups which can occur as the topological symmetry group of an embedding of the complete…

For each $n\leq 6$, we characterize all the groups which can occur as either the orientation preserving topological symmetry group or the topological symmetry group of some embedding of $K_n$ in $S^3$.

We classify all groups which can occur as the topological symmetry group of some embedding of the Heawood graph in $S^3$.

In this paper we complete the classification of topological symmetry groups for complete graphs $K_n$ by characterizing which $K_n$ can have a cyclic group, a dihedral group, or a subgroup of $D_m \times D_m$ where $m$ is odd, as its…

We give a necessary and sufficient condition for the mapping class group of the pair of the 3-sphere and a graph embedded in it to be isomorphic to the topological symmetry group of the embedded graph.

Assume that there is a free group action of automorphisms on a bipartite graph. If there is a perfect matching on the factor graph, then obviously there is a perfect matching on the graph. Surprisingly, the reversed is also true for…

We characterize which automorphisms of an arbitrary complete bipartite graph $K_{n,m}$ can be induced by a homeomorphism of some embedding of the graph in $S^3$.

We characterize all groups which can occur as the topological symmetry group or the orientation preserving topological symmetry group of some embedding of the Petersen graph in S^3.

Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…

The topological symmetry group $\mathrm{TSG}(\Gamma)$ of an embedding $\Gamma$ of a graph in $S^3$ is the subgroup of the automorphism group of the graph which is induced by homeomorphisms of $(S^3,\Gamma)$. If we restrict to orientation…

A graph $G$ is called \emph{symmetric with respect to a functional $F_G(P)$} defined on the set of all the probability distributions on its vertex set if the distribution $P^*$ maximizing $F_G(P)$ is uniform on $V(G)$. Using the…

We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group A_n which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group…

We classify all groups which can occur as the orientation preserving topological symmetry group of some embedding of a M\"{o}bius ladder graph in $S^3$.

It is known that the canonical double cover of any connected nonbipartite graph have an automorphism group of the form $H \rtimes \mathbb{Z}_2$, where $H$ is the set of automorphism which preserve bipartite parts. We construct connected…

We show that if the two parts of a finite bipartite graph have the same degree sequence, then there is a bipartite graph, with the same degree sequences, which is symmetric, in that it has an involutive graph automorphism that interchanges…

The regular embeddings of complete bipartite graphs $K_{n,n}$ in orientable surfaces are classified and enumerated, and their automorphism groups and combinatorial properties are determined. The method depends on earlier classifications in…