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

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. Many interconnection networks such as hypercube-like interconnection networks can be represented in the form of G0⊕G1 connecting two lower dimensional networks G0 and G1. 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 , 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.