3 citations · 8 across the 6 of their papers we have counts for
6 papers
On the number of generators of groups acting arc-transitively on graphs
Marco Barbieri, Pablo Spiga
Given a finite connected graph and a group acting transitively on the vertices of , we prove that the number of vertices of and the cardinality of are bounded ab…
On the proportion of derangements and on suborbits in finite transitive groups
Marco Barbieri, Pablo Spiga
We find a lower bound on the proportion of derangements in a finite transitive group that depends on the minimal nontrivial subdegree. As a consequence, we prove that, if is a…
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…
On the order of semiregular automorphisms of cubic vertex-transitive graphs
Marco Barbieri, Valentina Grazian, Pablo Spiga
We prove that, if is a finite connected cubic vertex-transitive graph, then either there exists a semiregular automorphism of of order at least , or the number of vertic…
On the number of fixed edges of automorphisms of vertex-transitive graphs of small valency
Marco Barbieri, Valentina Grazian, Pablo Spiga
We prove that, if is a finite connected -valent vertex-transitive, or -valent vertex- and edge-transitive graph, then either is part of a well-understood family of gr…
On the Cayleyness of Praeger-Xu graphs
Marco Barbieri, Valentina Grazian, Pablo Spiga
We give a sufficient and necessary condition for a Praeger-Xu graph to be a Cayley graph.