Abstract
Since the growing size of networks increases their vulnerability to component failures, fault tolerance is specially vital for interconnection networks. In the case of vertex failures, the connectivity is a classical measure for the fault tolerance of a network. Assume G = (V, E) is a connected graph. F⊆ E is a subset, if G - F is not connected and minimum degree δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G-F</sub> ≥ k, then we call F is a k-restricted edge cut. k-restricted edge connectivity λ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sup> (G) is the number of edges in a minimum k-restricted edge cut. The k-restricted vertex connectivity K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sup> (G) can be defined similarly. The k-restricted edge or vertex connectivity of crossed cubes CQ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> for small k are determined. And we also prove other properties of CQ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> .
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