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

Jung-Heum Park, Hyeong-Seok Lim, Hee-Chul Kim
2007 Theoretical Computer Science  
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
more » ... 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.
doi:10.1016/j.tcs.2007.02.029 fatcat:axbefevrvrdodblnmr6x3wmfeq