On groups with specified quotient power graphs

Abstract

In this paper we study some relations between the power and quotient power graph of a finite group‎. ‎These interesting relations motivate us to find some graph theoretical properties of the quotient‎ ‎power graph and the proper quotient power graph of a finite group $G$‎. ‎In addition‎, ‎we classify those groups whose quotient (proper quotient) power graphs are isomorphic to trees or paths‎.