The Super Connectivity Of Folded Crossed Cubes And Restricted Connectivity Of Crossed Cubes

Given a connected graph G and non-negative integer h,the h-restricted connectivity?resp.h-restricted edge-connectivity?of G is the minimum cardinality of a set of vertices?resp.edges?in G,if exists,whose deletion disconnects G and the degree of each vertex in every remaining component is at least h.Especially,1-restricted connectivity?resp.1-restricted edge-connectivity?is called the super connectivity?resp.super edge-connectivity?.The h-restricted connectivity measure is a generalization of the traditional connectivity measure,and it improves the connectivity measurement accuracy.Moreover,studies have revealed that if a network possesses a restricted connectivity property,it is more reliable and demonstrates a lower node failure rate compared with other networks.The hypercube Q_nis widely known as one of the most popular interconnection networks for parallel computing systems.The crossed cube CQ_nis also a variant of hypercube.The n-dimensional folded crossed cube F CQ_n,introduced by Zhang [Folded-crossed hypercube: a complete interconnection network,J.Syst.Archit.47?2002?917-922],is obtained from the crossed cube CQ_nby adding extra 2^n-1edges.In this paper,First we show that the super connectivity and the super edge-connectivity of F CQ_nare 2n for n ? 4.Moreover,we show that 2-and 3-restricted connectivity of n-dimensional crossed cubes are respectively 4n-8 for n ? 4 and 8n-24 for n ? 5.