Fibers on a graph with local load sharing

We study a random fiber bundle model with tips of the fibers placed on a graph having co-ordination number 3. These fibers follow local load sharing with uniformly distributed threshold strengths of the fibers. We have studied the critical behaviour of the model numerically using a finite size scaling method and the mean field critical behaviour is established. The avalanche size distribution is also found to exhibit a mean field nature in the asymptotic limit.