14 citations · 80 across the 33 of their papers we have counts for
38 papers · 1 filter
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…
An infinite family of simple graphs underlying chiral, orientable reflexible and non-orientable rotary maps
Isabel Hubard, Primož Potočnik, Primož Šparl
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 Bašić, 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…
Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree
Antonio Montero, Primož Potočnik
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…
Vertex-primitive digraphs with large fixity
Marco Barbieri, Primož Potočnik
The relative fixity of a digraph is defined as the ratio between the largest number of vertices fixed by a nontrivial automorphism of and the number of vertices of . We…
Resolution of a conjecture about linking ring structures
Marston Conder, Luke Morgan, Primož Potočnik
An LR-structure is a tetravalent vertex-transitive graph together with a special type of a decomposition of its edge-set into cycles. LR-structures were introduced in a paper by P.…