On Conditional h-Vertex Connectivity of Some Networks

The conditional h-vertex connectivity of G is defined as the minimum cardinality |S| (S ⊂V (G)) such that G-S is disconnected and has minimum degree at least h. It is an important measure of fault tolerance of networks. In this paper, we prove the lower bound of conditional hvertex connectivity of any n-dimensional hypercube-like network. We also determine the conditional h-vertex connectivity of Crossed cubes, Locally twisted cubes, Möbius cubes which are the members of hypercube-like networks.