Superpower graphs of finite groups

For a finite group Formula: see text the superpower graph Formula: see text of Formula: see text is an undirected simple graph with vertex set Formula: see text and two vertices are adjacent in Formula: see text if and only if the order of one divides the order of the other in Formula: see text. The aim of this paper is to provide tight bounds for the vertex connectivity, discuss Hamiltonian-like properties of superpower graph of finite non-Abelian groups having an element of exponent order. We also give some general results about superpower graphs and their relation to other graphs such as the Gruenberg–Kegel graph.