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math.GR2025
Enhanced power graphs of finite groups with cograph structure
Daniela Bubboloni, Francesco Fumagalli, Cheryl E. Praeger
The enhanced power graph, , of a group has vertex set and two elements are adjacent if they generate a cyclic subgroup. In the case of finite groups, we ide…
math.GR2024
Critical groups and partitions of finite groups
Daniela Bubboloni, Nicolas Pinzauti
We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results abou…
math.GR2024
Critical classes of power graphs and reconstruction of directed power graphs
Daniela Bubboloni, Nicolas Pinzauti
In a graph , we consider the common closed neighbourhood of a subset of vertices and use this notion to introduce a Moore closure operator in We also consider the cl…