Restricted Vertex Connectivity of Harary Graphs

Abstract

A vertex cut that separates the connected graph into components such that every vertex in these components has at least \(g\) neighbors is an \(R^g\)-vertex-cut. \(R^g\)-vertex-connectivity, denoted by \(\kappa^g(G)\), is the cardinality of a minimum \(R^g\)-vertex-cut of \(G\). In this paper, we will determine \(\kappa^g\) and characterize the \(R^g\)-vertex-atom-part for the first and second type Harary graphs.