6 papers · 1 filter
Polyhedral Maps of Cubic Graphs with given Automorphism Groups
Ugo Detaille, Meike WeiÃ, Reymond Akpanya +1
L. Babai introduced a method for constructing a cubic graph whose automorphism group is isomorphic to a given finite group , obtained by modifying a corresponding Cayley graph o…
Strong Embeddings of Regular Graphs with Prescribed Automorphism Groups
Reymond Akpanya, Tom Goertzen, Meike WeiÃ
A classical theorem of Frucht states that every finite group occurs as the automorphism group of a finite graph. We prove an embedded analogue for regular graphs of arbitrary degre…
Strong Embeddings of 3-Connected Cubic Planar Graphs on Surfaces of non-negative Euler Characteristic
Meike WeiÃ, Meike Weiß, Alice C. Niemeyer
Whitney proved that 3-connected planar graphs admit a unique embedding on the sphere. In contrast, Enami investigated embeddings of 3-connected cubic planar graphs on non-spherical…
On 3-Connected Planar Graphs with Unique Orientable Circuit Double Covers
Meike WeiÃ, Reymond Akpanya, Alice C. Niemeyer
A circuit double cover of a bridgeless graph is a collection of even subgraphs such that every edge is contained in exactly two subgraphs of the given collection. Such a circuit do…
On 3-Connected Cubic Planar Graphs and their Strong Embeddings on Orientable Surfaces
Meike WeiÃ, Reymond Akpanya, Alice C. Niemeyer
Although the strong embedding of a 3-connected planar graph on the sphere is unique, can have different inequivalent strong embeddings on a surface of positive genus. If $G…
Interplay of Cubic Graphs and Simplicial Surfaces
Meike WeiÃ, Alice C. Niemeyer
Simplicial surfaces describe the incidence relations between vertices, edges and faces of triangulated 2-dimensional manifolds in a purely combinatorial way. By considering only th…