The minimal (edge) connectivity of some graphs of finite groups

In this paper, we classify all the finite groups [Formula: see text] such that the commuting graph [Formula: see text], order-sum graph [Formula: see text] and non-inverse graph [Formula: see text] are minimally edge connected graphs. We also classify all the finite groups [Formula: see text] for that, these graphs are minimally connected. We also classify some groups for that the co-prime graph [Formula: see text] has minimal edge connectedness. In final part, we classify all the finite groups [Formula: see text] for that co-prime graph [Formula: see text] is minimally connected.