On g-Extra Connectivity of Corona-Type Graph Products

Connectivity is one of the central ideas in graph theory, especially when it comes to building fault-tolerant networks. A cutset $S$ of $G$ is defined to be the set of vertices in $G$ whose removal disconnects the graph. An $R_g$ cutset of $G$ is a cutset whose removal disconnects the graph in such a way that each connected component has at least $g+1$ vertices. If $G$ has at least one $R_g$ cutset then the $g-$extra vertex connectivity (or the $g-$extra edge connectivity), denoted as ${\kappa }_g(G)$ (${\lambda }_g(G)$), is defined as the minimum cardinality of $R_g$ cutset. In this paper, we obtain the $g-$ extra connectivity of various corona type graph products edge corona, neighbourhood corona, subdivision vertex neighbourhood corona,subdivision edge neighbourhood corona and generalised corona product.