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 su…
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…