Toroidal Embeddings of Right Groups
نویسندگان
چکیده
In this note we study embeddings of Cayley graphs of right groups on surfaces. We characterize those right groups which have a toroidal but no planar Cayley graph, such that the generating system of the right group has a minimal generating system of the group as a factor.
منابع مشابه
On the flexibility of toroidal embeddings
Two embeddings Ψ1 and Ψ2 of a graph G in a surface Σ are equivalent if there is a homeomorphism of Σ to itself carrying Ψ1 to Ψ2. In this paper, we classify the flexibility of embeddings in the torus with representativity at least 4. We show that if a graph G has an embedding Ψ in the torus with representativity at least 4, then one of the following holds: (i) Ψ is the unique embedding of G in ...
متن کاملToroidal embeddings of abstractly planar graphs are knotted or linked
We give explicit deformations of embeddings of abstractly planar graphs that lie on the standard torus T 2 ⊂ R3 and that contain neither a nontrivial knot nor a nonsplit link into the plane. It follows that ravels do not embed on the torus. Our results provide general insight into properties of molecules that are synthesized on a torus.
متن کاملOn Embeddings of Circulant Graphs
A circulant of order n is a Cayley graph for the cyclic group Zn, and as such, admits a transitive action of Zn on its vertices. This paper concerns 2-cell embeddings of connected circulants on closed orientable surfaces. Embeddings on the sphere (the planar case) were classified by Heuberger (2003), and by a theorem of Thomassen (1991), there are only finitely many vertex-transitive graphs wit...
متن کاملSeparating Cycles in Doubly Toroidal Embeddings
We show that every 4-representative graph embedding in the double torus contains a noncontractible cycle which separates the surface into two pieces. This improves a result of Zha and Zhao for general orientable surfaces, in which the same conclusion holds for 6-representative graph embeddings. Noncontractible separating cycles have been studied because they provide a way to do induction on the...
متن کاملSpanning subsets of toroidal and Klein bottle embeddings
Let Φ be an embedding of graph G in a surface S. If there exists a subset K of S bounded by a subgraph of G which contains all the vertices of G, then K is called a spanning subset of Φ. Examples of spanning subsets include spanning discs, spanning annuli with some number of holes (called planarizing sets in some papers). A spanning subset may provide a simpler structure but still contain enoug...
متن کامل