On Super and Restricted Connectivity of Some Interconnection Networks

The super (resp., edge-) connectivity of a connected graph is the minimum cardinality of a vertex-cut (resp., an edge-cut) whose removal does not isolate a vertex. In this paper, we consider the two parameters for a special class of graphs G(G0, G1; M), proposed by Chen et al [Applied Math. and Computation, 140 (2003), 245-254], obtained from two k-regular k-connected graphs G0 and G1 with the same order by adding a perfect matching between their vertices. Our results improve ones of Chen et al. As applications, the super connectivity and the super edge-connectivity of the n-dimensional hypercube, twisted cube, cross cube, Möbius cube and locally twisted cube are all 2n− 2.