-Extraconnectivities of hypercube-like networks

Abstract: A subset of vertices X is said to be a cutset if is not connected. A cutset X is called an -cutset if every component of has at least vertices. If G has at least one -cutset, the g-extraconnectivity of G is then defined as the minimum cardinality over all -cutsets of G. In this paper, we first show that the 2-extraconnectivity of an n-dimensional hypercube-like network is for . This improves on the previously best known result, which showed that the 2-extraconnectivity of an n-dimensional hypercube-like network is for . We further demonstrate that the 3-extraconnectivity of an n-dimensional hypercube-like network is for . Based on the above results, the 2-extraconnectivity and 3-extraconnectivity of several interconnection networks, including hypercubes, twisted cubes, crossed cubes, Möbius cubes, locally twisted cubes, generalized twisted cubes, recursive circulants, and Mcubes, can be determined efficiently. [Copyright &y& Elsevier]