  The effect of randomness on critical behavior is a crucial subject in
condensed matter physics due to the the presence of impurity in any real
material. We presently probe the critical behaviour of the antiferromagnetic
(AF) Ising model on rewired square lattices with random connectivity. An extra
link is randomly added to each site of the square lattice to connect the site
to one of its next-nearest neighbours, thus having different number of
connections (links). Average number of links (ANOL) $\kappa$ is fractional,
varied from 2 to 3, where $\kappa = 2$ associated with the native square
lattice. The rewired lattices possess abundance of triangular units in which
spins are frustrated due to AF interaction. The system is studied by using
Monte Carlo method with Replica Exchange algorithm. Some physical quantities of
interests were calculated, such as the specific heat, the staggered
magnetization and the spin glass order parameter (Edward-Anderson parameter).
We investigate the role played by the randomness in affecting the existing
phase transition and its interplay with frustration to possibly bring any spin
glass (SG) properties. We observed the low temperature magnetic ordered phase
(N\'eel phase) preserved up to certain value of $\kappa$ and no indication of
SG phase for any value of $\kappa$.
