  The Apollonian networks display the remarkable power-law and small-world
properties as observed in most realistic networked systems. Their dual graphs
are extended Tower of Hanoi graphs, which are obtained from the Tower of Hanoi
graphs by adding a special vertex linked to all its three extreme vertices. In
this paper, we study analytically maximum matchings and minimum dominating sets
in Apollonian networks and their dual graph- s, both of which have found vast
applications in various fields, e.g. structural controllability of complex
networks. For both networks, we determine their matching number, domination
number, the number of maximum matchings, as well as the number of minimum
dominating sets.
