Fault tolerant routing in star graph networks in the forbidden fault model

It is well known that star graphs are strongly resilient like the n cubes in the sense that they are optima[ly fault tolerant and the fault diameter is increased only by one in the presence of maximum number of allowable faults [1, 2]. Star graphs have also been investigated under the conditions of forbidden faulty sets [3] where all the neighbors of any node cannot be faulty simultaneously; we have shown [4] that under these conditions star graphs can tolerate up to (2n - 5) faulty nodes and the fault diameter is increased only by 2 in the worst case in presence of maximum number of faults. Thus, star graphs enjoy the similar property of strong resilience under forbidden faulty sets like the n-cubes. Our purpose in the present paper is to develop shortest routing algorithms between arbitrary pair of nodes under this restricted fault model.