Study on Leavitt path algebras and associated Grothendieck groups for directed enhanced power graphs

Abstract

In this paper, we define directed enhanced power graphs for finite groups and study some graph-theoretic properties. Moreover, we investigate several algebraic properties of Leavitt path algebras of the directed enhanced power graphs and also of the directed punctured enhanced power graphs. We also compute Grothendieck groups of the Leavitt path algebras of directed punctured enhanced power graphs for cyclic groups and give partial answers to “the algebraic Kirchberg–Phillips question”.