  We propose two types of evolving networks: evolutionary Apollonian networks
(EAN) and general deterministic Apollonian networks (GDAN), established by
simple iteration algorithms. We investigate the two networks by both simulation
and theoretical prediction. Analytical results show that both networks follow
power-law degree distributions, with distribution exponents continuously tuned
from 2 to 3. The accurate expression of clustering coefficient is also given
for both networks. Moreover, the investigation of the average path length of
EAN and the diameter of GDAN reveals that these two types of networks possess
small-world feature. In addition, we study the collective synchronization
behavior on some limitations of the EAN.
