A. Arockiaraj, S. Klav¾ar, P. Manuel, E. Thomas, A. Xavier
Strong geodetic problems in networks
Discussiones Mathematicae Graph Theory
Received 17.07.2017, Revised 19.03.2018, Accepted 19.03.2018, doi: 10.7151/dmgt.2139
In order to model certain social network problems, the strong geodetic problem and its related invariant, the strong geodetic number, are introduced. The problem is conceptually similar to the classical geodetic problem but seems intrinsically more difficult. The strong geodetic number is compared with the geodetic number and with the isometric path number. It is determined for several families of graphs including Apollonian networks. Applying Sierpiński graphs, an algorithm is developed that returns a minimum path cover of Apollonian networks corresponding to the strong geodetic number. It is also proved that the strong geodetic problem is NP-complete.