Does there exist any results on the vertex connectivity of join of two graphs?
If $G_1$ and $G_2$ are two graphs what can we say about the vertex connectivity of $G_1\lor G_2$ where $G_1\lor G_2$ is the join of two graphs$G_1$ and $G_2$? The join of $G_1$ and $G_1$ is the graph obtained from the disjoint union of $G_1$ and $G_2$ by adding all edges between $V(G_1)$ and $V(G_2)$.
If $\kappa(G)$ denotes vertex connectivity of a graph $G$ how is $\kappa(G_1\lor G_2)$ related to $\kappa(G_1)$ and $\kappa(G_2)$?
