The extreme vertices of the power graph of a group

Abstract

For a fixed finite group G, the power graph of G was defined to be the simple graph Γ(G) whose vertex set V(Γ(G))=G, and edge set E(Γ(G))={xy: either x=yn or y=xn for some integer n}. In this paper the extreme vertices of the power graph of abelian groups, dihedral groups and dicyclic groups have been characterized.

Keywords

• Power graph of a group
• Extreme vertices
• Abelian group
• Dihedral group