On g-Extra Connectivity of Corona-Type Graph Products
Abstract
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 Rg 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 Rg cutset then the g-extra vertex connectivity (or the g-extra edge connectivity), denoted as g(G) (λg(G)), is defined as the minimum cardinality of Rg 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.
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