Panconnectivity for interconnection networks with faulty elements

Let G 0 and G 1 be two graphs with the same vertices. The new graph G(G 0, G 1; M) is a graph with the vertex set V (G 0).V(G 1) and the edge set E(G 0).E(G 1).M, where M is an arbitrary perfect matching between the vertices of G 0 and G 1, i.e., a set of cross edges with one endvertex in G 0 and the other endvertex in G 1. In this paper, we will show that if G 0 and G 1 are f-fault q-panconnected, then for any f . 2, G(G 0, G 1; M) is (f + 1)-fault (q + 2)-panconnected