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Super Spanning Connectivity of the Folded Divide-and-SwapCube

Author

Listed:
  • Lantao You

    (School of Information Engineering, Suzhou Industrial Park Institute of Services Outsourcing, Suzhou 215123, China
    Suzhou Industrial Park Human Resources Development Co., Ltd., Suzhou 215005, China
    Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, Suzhou 215006, China)

  • Jianfeng Jiang

    (School of Information Engineering, Suzhou Industrial Park Institute of Services Outsourcing, Suzhou 215123, China)

  • Yuejuan Han

    (School of Computer Science and Technology, Soochow University, Suzhou 215006, China)

Abstract

A k * -container of a graph G is a set of k disjoint paths between any pair of nodes whose union covers all nodes of G . The spanning connectivity of G , κ * ( G ) , is the largest k , such that there exists a j * -container between any pair of nodes of G for all 1 ≤ j ≤ k . If κ * ( G ) = κ ( G ) , then G is super spanning connected. Spanning connectivity is an important property to measure the fault tolerance of an interconnection network. The divide-and-swap cube D S C n is a newly proposed hypercube variant, which reduces the network cost from O ( n 2 ) to O ( n log 2 n ) compared with the hypercube and other hypercube variants. The folded divide-and-swap cube F D S C n is proposed based on D S C n to reduce the diameter of D S C n . Both D S C n and F D S C n possess many better properties than hypercubes. In this paper, we investigate the super spanning connectivity of F D S C n where n = 2 d and d ≥ 1 . We show that κ * ( F D S C n ) = κ ( F D S C n ) = d + 2 , which means there exists an m -DPC(node-disjoint path cover) between any pair of nodes in F D S C n for all 1 ≤ m ≤ d + 2 .

Suggested Citation

  • Lantao You & Jianfeng Jiang & Yuejuan Han, 2023. "Super Spanning Connectivity of the Folded Divide-and-SwapCube," Mathematics, MDPI, vol. 11(11), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2581-:d:1164213
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