The geodetic problem was introduced by Harary et al. [17]. In order to model some social network problems, a similar problem is introduced in this paper and named the strong geodetic problem. The problem is solved for complete Apollonian networks. It is also proved that in general the strong geodetic problem is NP-complete.

originally sited in the genitals, but then altered to the side) refuses to heal and he has excruciating night pains, relieved only by baths and balsams. And the authors peel off layer after layer of Wagner's subtleties to support their case-his verbal puns, for instance, and the association between syphilis and flowers (no reader of Baudelaire or Huysmans would see the flower maidens who try to...

We present a simple algorithm that produces a so called growing Ramified Random Apollonian Networks (R-RAN) in any dimension d. Analytical derivations show that these networks still exhibit small-word and scale-free characteristics. To characterize further the structure of R-RAN, we introduce new parameters that we refer to as the parallel degree and the ramification coefficient, that determine...

We study the percolation problem on the Apollonian network model. The Apollonian networks display many interesting properties commonly observed in real network systems, such as small-world behavior, scale-free distribution, and a hierarchical structure. By taking advantage of the deterministic hierarchical construction of these networks, we use the real-space renormalization-group technique to ...