Hamiltonian connectivity of the WK-recursive network with faulty nodes

  • Authors:
  • Jung-Sheng Fu

  • Affiliations:
  • Department of Electronic Engineering, National United University, 1, Lien Da, Kung-Ching Li, Miaoli 36003, Taiwan

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2008

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Abstract

A graph G is said to be Hamiltonian-connected if there is a Hamiltonian path between every two distinct nodes of G. Let F denote the set of faulty nodes of G. Then, G is |F|-node Hamiltonian-connected if G-F is Hamiltonian-connected. We use K(d,t) to denote a WK-recursive network of level t, each of whose basic modules is a d-node complete graph. Compared with other networks, it is rather difficult to construct a Hamiltonian path between two arbitrary nodes in a faulty WK-recursive network. In this paper, we show that K(d,t) is (d-4)-node Hamiltonian-connected. Since the connectivity of K(d,t) is d-1, the result is optimal in the worst case.