3 papers
math.CO2026
The base size of vertex-transitive cubic graphs
Marco Barbieri, Luca Sabatini, Pablo Spiga
We prove that if is a finite connected vertex-transitive cubic graph, then either , or is a split Praeger--Xu graph, or there exist two vertices and $Î…
math.GR2026
On the expected value of energy in groups
Marco Barbieri, Marusa Lekše, Andoni Zozaya
We obtain explicit upper and lower bounds for the expected action energy associated with a pair of subsets sampled uniformly at random from a permutation group…
math.GR2024
Elementary proofs of the diameter bounds for the power graphs
Marco Barbieri, Kamilla Rekvényi
We give a simplified version of the proofs that, outside of their isolated vertices, the complement of the enhanced power graph and of the power graph are connected of diameter at…