The Minimal (Edge) Connectivity of Some Graphs of Finite Groups

In this paper, we classify all the finite groups $G$ such that the commuting graph ${\mathrm{\Gamma }}_C(G)$, order-sum graph ${\mathrm{\Gamma }}_{OS}(G)$ and non-inverse graph ${\mathrm{\Gamma }}_{NI}(G)$ 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 ${\mathrm{\Gamma }}_{CP}(G)$ has minimal edge connectedness. In final part, we classify all the finite groups $G$ for that co-prime graph ${\mathrm{\Gamma }}_{CP}(G)$ is minimally connected.