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, Korea;School of Electronics and Computer Engineering, Chonnam National University, Korea;Computer Science and Information Communications Engineering Division, Hankuk University of Foreign Studies, Korea
Venue:
ISPA'06 Proceedings of the 2006 international conference on Frontiers of High Performance Computing and Networking
Year:
2006

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Abstract

In this paper, we deal with the graph G0 ⊕G1 obtained from merging two graphs G0 and G1 with n vertices each by n pairwise nonadjacent edges joining vertices in G0 and vertices in G1. The main problems studied are how fault-panconnectivity and fault-pancyclicity of G0 and G1 are translated into fault-panconnectivity and fault-pancyclicity of G0 ⊕G1, respectively. Applying our results to a subclass 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.