Optimal 1-edge fault-tolerant designs for ladders
A graph G* is 1-edge fault-tolerant with respect to a graph G, denoted by 1-EFT(G), if every graph obtained by removing any edge from G* contains G. A1-EFT(G) graph is optimal if it contains the minimum number of edges among all 1-EFT(G) graphs. The kth ladder graph, L-k, is defined to be the cartesian product of the P-k and P-2 where P-n is the n-vertex path graph. In this paper, we present several 1-edge fault-tolerant graphs with respect to ladders. Some of these graphs are proven to be optimal. (C) 2002 Elsevier Science B.V. All rights reserved.
ladders cartesian product edge fault tolerance meshes fault tolerance