8 papers · 1 filter
Polyhedral Maps of Cubic Graphs with given Automorphism Groups
Ugo Detaille, Meike Weiß, 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 Weiß
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…
On 3-Connected Planar Graphs with Unique Orientable Circuit Double Covers
Meike Weiß, 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…
A Census of Edge-transitive Surfaces
Reymond Akpanya
In this paper, we study edge-transitive surfaces, i.e. triangulated 2-dimensional manifolds whose automorphism groups act transitively on the edges of these triangulated surfaces.…
On 3-Connected Cubic Planar Graphs and their Strong Embeddings on Orientable Surfaces
Meike Weiß, 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…
A census of face-transitive surfaces
Reymond Akpanya, Jonathan Spreer
A face-transitive surface is a triangulated 2-dimensional manifold whose automorphism group acts transitively on its set of triangles. In this paper, we investigate this class of h…
Construction of Toroidal Polyhedra corresponding to perfect Chains of wild Tetrahedra
Reymond Akpanya, Vanishree Krishna Kirekod, Alice C. Niemeyer +1
In 1957, Steinhaus proved that a chain of regular tetrahedra, meeting face-to-face and forming a closed loop does not exist. Over the years, various modifications of this statement…
Topologically Interlocking Blocks inside the Tetroctahedrille
Reymond Akpanya, Tom Goertzen, Alice C. Niemeyer
A topological interlocking assembly consists of rigid blocks together with a fixed frame, such that any subset of blocks is kinematically constrained and therefore cannot be remove…