Abstract
In this paper, we explore the 2-extraconnectivity of a special class of graphs G ( G 0 , G 1 ; M ) proposed by Chen et al. [Y.-C. Chen, J.J.M. Tan, L.-H. Hsu, S.-S. Kao, Super-connectivity and super edge-connectivity for some interconnection networks, Applied Mathematics and Computation 140 (2003) 245–254]. As applications of the results, we obtain that the 2-extraconnectivities of several well-known interconnection networks, such as hypercubes, twisted cubes, crossed cubes, Möbius cubes and locally twisted cubes, are all equal to 3 n − 5 when their dimension n is not less than 8. That is, when n ⩾ 8 , at least 3 n − 5 vertices must be removed to disconnect any one of these n-dimensional networks provided that the removal of these vertices does not isolate a vertex or an edge.
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