A kind of conditional connectivity of bubble-sort networks
[Objective]As one of intensively-investigated research topics in network fault tolerance,the bubble-sort network secures good properties,such as high symmetry and recursive structure.Herein,we determine the h-extra r-component edge connectivity of bubble-sort networks.[Methods]The bubble-sort graph Bn can be partitioned into n subgraphs Bn(i),where Bn(i)denotes the induced subgraph by the set of vertex{x1x2…xn:xn=i} for 1≤ i≤n and isomorphic to Bn-1.According to its structural characteristics,we use mathematical induction to infer and prove main results.[Results]We determine the h-extra r-component edge connectivity of bubble-sort networks,i.e.cλ23(Bn)=4n-10(n≥4).[Conclusions]The conditional connectivity can be used to measure the reliability of a network.We investigate a type of conditional connectivity of bubble-sort networks,and plan to continue studying other conditional connectivities of bubble-sort networks in the future.
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