On g-Extra Connectivity of Corona-Type Graph Products

TL;DR

This paper investigates the g-extra connectivity of various corona-type graph products, providing formulas and results that enhance understanding of fault tolerance in network design.

Contribution

It introduces the g-extra connectivity for multiple corona-type graph products, extending existing theories in graph connectivity and fault tolerance analysis.

Findings

Derived g-extra connectivity formulas for edge corona

Analyzed g-extra connectivity for neighbourhood corona

Extended results to subdivision and generalized corona 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 $R_g$ 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.