Restricted Connectivity for Some Interconnection Networks

A vertex-cut of a connected graph is called a restricted vertex-cut if no vertex of the graph satisfies . The restricted connectivity of the graph is the cardinality of a minimum restricted vertex-cut of ; this is a more refined index than the connectivity parameter . In this paper, we prove that , where is a -regular and maximally connected graph with girth ; and , where is a -regular and maximally connected graph with girth for . Furthermore, we determine the restricted connectivity of a class of minimal Abelian Cayley graphs.