6 papers
Computing the Hamiltonian compression factors of cubic graphs
Marston Conder, Gregor Potocnik, Primoz Potocnik
We present an algorithm for computing Hamiltonian cycles that are invariant under a graph automorphism acting on them as a rotation. We also present an application of this algorith…
Separating subsets from their images
Marco Barbieri, MaruÅ¡a LekÅ¡e, Primož PotoÄnik +1
Let be a transitive permutation group acting on . In this paper, we introduce and study the parameter , which denotes the size of the smallest set of points …
Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree
Antonio Montero, Primož PotoÄnik
The motion of a graph is the minimum number of vertices that are moved by a non-trivial automorphism. Equivalently, it can be defined as the minimal degree of its automorphism grou…
An infinite family of simple graphs underlying chiral, orientable reflexible and non-orientable rotary maps
Isabel Hubard, Primož PotoÄnik, Primož Å parl
In this paper, we provide the first known infinite family of simple graphs, each of which is the skeleton of a chiral map, a skeleton of a reflexible map on an orientable surfaces,…
Nut digraphs
Nino BaÅ¡iÄ, Patrick W. Fowler, Maxine M. McCarthy +1
A nut graph is a simple graph whose kernel is spanned by a single full vector (i.e. the adjacency matrix has a single zero eigenvalue and all non-zero kernel eigenvectors have no z…
Cubic vertex-transitive graphs of girth six
Primož PotoÄnik, JanoÅ¡ Vidali
In this paper, a complete classification of finite simple cubic vertex-transitive graphs of girth is obtained. It is proved that every such graph, with the exception of the Des…