Edge-maximality of power graphs of finite cyclic groups

Abstract

We show that among all finite groups of any given order, the cyclic group of that order has the maximum number of edges in its power graph. Contains corrections to published version.

second set of corrections to technical lemmas, no changes to main result

Cited by in corpus (4)

• Vertex connectivity of the power graph of a finite cyclic group
• The degree of a vertex in the power graph of a finite abelian group
• On the minimum cut-sets of the power graph of a finite cyclic group
• Group With Maximum Undirected Edges in Directed Power Graph Among All Finite Non-Cyclic Nilpotent Groups