Super Spanning Connectivity of the Folded Divide-and-SwapCube

Lantao You, Jianfeng Jiang and Yuejuan Han ()
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Lantao You: School of Information Engineering, Suzhou Industrial Park Institute of Services Outsourcing, Suzhou 215123, 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

Mathematics, 2023, vol. 11, issue 11, 1-12

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 .

Keywords: folded divide-and-swap cube; node-disjoint path cover; interconnection network; Hamiltonian; super spanning connectivity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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