1 citations · 1 across the 13 of their papers we have counts for
15 papers
Highly symmetric unstable maniplexes
Isabel Hubard, Micael Toledo
A maniplex of rank n s an n-valent properly edge-coloured graph that generalises, simultaneously, maps on surfaces and abstract polytopes. The problem of stability in maniplexes is…
Cubic vertex-transitive graphs of girth seven
Maruša Lekše, Micael Toledo
In this paper we classify cubic vertex-transitive graphs of girth , based on their signature. Such a graph is either a truncation of an arc-transitive dihedral scheme on a -r…
Orbits of consistent walk in dart-transitive maps
Micael Toledo, Alejandra Ramos, Primoz Potocnik +1
In a simple graph, a shunt is a symmetry which sends an edge to an incident edge (without fixing their shared vertex). The orbit of this edge under the shunt forms a consistent cyc…
Chiral extensions of regular toroids
Antonio Montero, Micael Toledo
Abstract polytopes are combinatorial objects that generalise geometric objects such as convex polytopes, maps on surfaces and tilings of the space. Chiral polytopes are those abstr…
Sparse groups need not be semisparse
Isabel Hubard, Micael Toledo
In 1999 Michael Hartley showed that any abstract polytope can be constructed as a double coset poset, by means of a C-group $\C$ and a subgroup $N \leq \C$. Subgroups $N \leq \C$ t…
Transitive cornerations in maps
Primoz Potocnik, Alejandra Ramos-Rivera, Micael Toledo +1
A corner in a map is an edge-vertex-edge triple consisting of two distinct edges incident to the same vertex. A corneration is a set of corners that covers every arc of the map exa…
Faithful and thin non-polytopal maniplexes
Dimitri Leemans, Micael Toledo
Maniplexes are coloured graphs that generalise maps on surfaces and abstract polytopes. Each maniplex uniquely defines a partially ordered set that encodes information about its st…
Maniplexes with automorphism group
Dimitri Leemans, Micael Toledo
A maniplex of rank is a combinatorial object that generalises the notion of a rank abstract polytope. A maniplex with the highest possible degree of symmetry is called refl…
Cubic vertex-transitive graphs admitting automorphisms of large order
Primož Potočnik, Micael Toledo
A connected graph of order admitting a semiregular automorphism of order is called a -multicirculant. Highly symmetric multicirculants of small valency have been exten…
On orders of automorphisms of vertex-transitive graphs
Primoz Potocnik, Micael Toledo, Gabriel Verret
In this paper we investigate orders, longest cycles and the number of cycles of automorphisms of finite vertex-transitive graphs. In particular, we show that the order of every aut…
Finite cubic graphs admitting an cyclic group of automorphisms with at most three orbits on vertices
Primoz Potocnik, Micael Toledo
The theory of voltage graphs has become a standard tool in the study graphs admitting a semiregular group of automorphisms. We introduce the notion of a cyclic generalised voltage…
Generalised Voltage Graphs
Primoz Potocnik, Micael Toledo
A graph with a semiregular group of automorphisms can be thought of as the derived cover arising from a voltage graph. Since its inception, the theory of voltage graphs and their d…
Classification of cubic vertex-transitive tricirculants
Primož Potočnik, Micael Toledo
A finite graph is called a tricirculant if admits a cyclic group of automorphism which has precisely three orbits on the vertex-set of the graph, all of equal size. We classify all…
An existence result on two-orbit maniplexes
Daniel Pellicer, Primož Potočnik, Micael Toledo
A maniplex of rank n is a connected, n-valent, edge-coloured graph that generalises abstract polytopes and maps. If the automorphism group of a maniplex M partitions the vertex-set…
Symmetry Type Graphs of Abstract Polytopes and Maniplexes
Gabe Cunningham, Maria del Rio Francos, Isabel Hubard +1
A -orbit maniplex is one that has orbits of flags under the action of its automorphism group. In this paper we extend the notion of symmetry type graphs of maps to that of m…