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doi:10.1016/S0020-0190(97)00003-3 
Copyright © 1997 Published by Elsevier Science B.V.
Faithful 1-edge fault tolerant graphs*1
Received 2 April 1996;
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Abstract
A graph G* is 1-edge fault tolerant with respect to a graph G, denoted by 1-EFT(G), if any graph obtained by removing an edge from G* contains G. A 1-EFT(G) graph is said to be optimal if it contains the minimum number of edges among all 1-EFT(G) graphs. Let Gi* be 1-EFT(Gi) for i = 1,2. It can be easily verified that the cartesian product graph G*1 × G2* is 1-edge fault tolerant with respect to the cartesian product graph G1 × G2. However, G1* × G2* may contain too many edges; hence it may not be optimal for many cases. In this paper, we introduce the concept of faithful graph with respect to a given graph, which is proved to be 1-edge fault tolerant. Based on this concept, we present a construction method of the 1-EFT graph for the cartesian product of several graphs. Applying this construction scheme, we can obtain optimal 1-edge fault tolerant graphs with respect to n-dimensional tori C(m1, m2,…, mn), where mi 
4 are even integers for all 1 
i n.
Author Keywords: Cartesian product; Kronecker product; Edge fault tolerance; Meshes; Tori
