  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.
