Finite groups whose intersection power graphs are toroidal and projective-planar

Abstract

The intersection power graph of a finite group GG is the graph whose vertex set is GG, and two distinct vertices xx and yy are adjacent if either one of xx and yy is the identity element of GG, or ⟨x⟩∩⟨y⟩\langle x\rangle \cap \langle y\rangle is non-trivial. In this paper, we completely classify all finite groups whose intersection power graphs are toroidal and projective-planar.

Keywords

• intersection power graph
• finite group
• genus
• 05c25
• 05c10