Restricted Vertex Connectivity of Harary Graphs

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, denote 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.