On f-fault tolerant arc-forwarding and optical indices of all-optical folded hypercubes

We construct a leveled f-fault tolerant routing for a class of the folded hypercube networks. This routing achieves a lower bound established by Gupta in [A. Gupta, J. Man˘uch, L. Stacho, Fault tolerant forwarding and optical indices: A design theory approach, J. Combin. Designs 14 (2006) 25–40] and therefore, yields the exact value of the f-fault tolerant arc-forwarding index for this class. In addition, again by applying this routing together with the Brook's Theorem [J.A. Bondy, U.S.R. Murty, Graph Theory with Applications, The Macmillan Press Ltd., 1976], an upper bound for the f-fault tolerant optical index is also established.