4.6 Article

Disjoint paths in the enhanced hypercube with a faulty subgraph

Journal

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
Volume 69, Issue 2, Pages 1343-1354

Publisher

SPRINGER HEIDELBERG
DOI: 10.1007/s12190-022-01794-z

Keywords

Interconnection network; Enhanced hypercube; Disjoint paths; Strong Menger connectivity

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The paper discusses the problem of embedding internally disjoint paths in an enhanced hypercube and proves that the subgraph obtained by deleting the faulty subnetwork from the enhanced hypercube remains strong Menger connected even when the network has faults.
Problems about embedding of disjoint paths in interconnection networks have received much attention in recent years. A connected graph G is strong Menger connected if there are min{d(G)(u), d(G)(v)} internally disjoint paths joining any two distinct vertices u and v in G. The enhanced hypercube Q(n, k) is an important variant of the hypercube Q(n) that retains many desirable properties of the hypercube. In order to study its fault tolerance, we consider the problem of embedding internally disjoint paths in an enhanced hypercube when part of the network is faulty. We show that the subgraph obtained from the enhanced hypercube Q(n, k) (2 <= k <= n) by deleting the vertices of a faulty subnetwork Q(s) (1 <= s <= n - 1) or Q(s, k) (k <= s <= n - 1) is strong Menger connected.

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