  We consider the ordering dynamics of the Ising model on a square lattice
where an additional fixed number of bonds connect any two sites chosen
randomly. The total number of shortcuts added is controlled by two parameters
$p$ and $\alpha$. The structural properties of the network are investigated
which show that that the small world behaviour is obtained along the line
$\alpha=\frac{\ln (N/2p)}{\ln N}$, which separates regions with ultra small
world like behaviour and short ranged lattice like behaviour. We obtain a rich
phase diagram in the $p-\alpha$ plane showing the existence of different types
of active and absorbing states to which Ising model evolves and their
boundaries.
