5 papers
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…