Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements

  • Authors:

  • Jung-Heum Park;Hyeong-Seok Lim;Hee-Chul Kim

  • Affiliations:

  • School of Computer Science and Information Engineering, The Catholic University of Korea, Republic of Korea;School of Electronics and Computer Engineering, Chonnam National University, Republic of Korea;Computer Science and Information Communications Engineering Division, Hankuk University of Foreign Studies, Republic of Korea

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2007

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Abstract

In this paper, we deal with the graph G"0@?G"1 obtained from merging two graphs G"0 and G"1 with n vertices each by n pairwise nonadjacent edges joining vertices in G"0 and vertices in G"1. The main problems studied are how fault-panconnectivity and fault-pancyclicity of G"0 and G"1 are translated into fault-panconnectivity and fault-pancyclicity of G"0@?G"1, respectively. Many interconnection networks such as hypercube-like interconnection networks can be represented in the form of G"0@?G"1 connecting two lower dimensional networks G"0 and G"1. Applying our results to a class of hypercube-like interconnection networks called restricted HL-graphs, we show that in a restricted HL-graph G of degree m(=3), each pair of vertices are joined by a path in G@?F of every length from 2m-3 to |V(G@?F)|-1 for any set F of faulty elements (vertices and/or edges) with |F|@?m-3, and there exists a cycle of every length from 4 to |V(G@?F)| for any fault set F with |F|@?m-2.