We classify planar graphs and complete power graphs of groups and show that the only infinite group

with a complete power graph is the Prüfer group Z_{p^∞}. Clique and chromatic numbers and the automorphism group ...

The aim of this paper is to identify complete power graphs of groups and compute their clique number and show that power graphs are perfect. Moreover, automorphism of the power graph of cyclic groups is determined here.

The power graph P (G) of a finite group G is a graph whose vertex set is the group G and distinct

elements x ,y ∈ G are adjacent if one is a power of the other, that is, x and y are adjacent if x ∈ ⟨y⟩or

y ...