In this paper, we classify all the finite groups G such that the commuting graph Γ C (G), order-sum graph Γ OS (G) and non-inverse graph Γ NI (G) are minimally edge connected graphs. We also classify all the finite groups G for that, these graphs are minimally connected. We also classify some groups for that the co-prime graph Γ CP (G) has minimal edge connectedness. In final part, we classify all the finite groups G for that co-prime graph Γ CP (G) is minimally connected.
Malviy et al. (Fri,) studied this question.