  Networks are ubiquitous in diverse real-world systems. Many empirical
networks grow as the number of nodes increases with time. Percolation
transitions in growing random networks can be of infinite order. However, when
the growth of large clusters is suppressed under some effects, e.g., the
Achlioptas process, the transition type changes to the second order. However,
analytical results for the critical behavior, such as the transition point,
critical exponents, and scaling relations are rare. Here, we derived them
explicitly as a function of a control parameter $m$ representing the
suppression strength using the scaling ansatz. We then confirmed the results by
solving the rate equation and performing numerical simulations. Our results
clearly show that the transition point approaches unity and the order-parameter
exponent $\beta$ approaches zero algebraically as $m \to \infty$, whereas they
approach these values exponentially for a static network. Moreover, the upper
critical dimension becomes $d_u=4$ for growing networks, whereas it is $d_u=2$
for static ones.
