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

Maximum matchings and minimum dominating sets in Apollonian networks and extended Tower of Hanoi graphs