On groups with specified quotient power graphs

Abstract

Abstract. In this paper we study some relations between the power andquotient power graph of a finite group. These interesting relations motivateus to find some graph theoretical properties of the quotient power graphand the proper quotient power graph of a finite group G. In addition, weclassify those groups whose quotient (proper quotient) power graphs areisomorphic to trees or paths.

Keywords

• Quotient power graph
• Fitting subgroup
• full exponent