Abstract: 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.Keywords: geodetic problem, strong geodetic problem, Apollonian networks, Sierpiński graphs, computational complexityPublished in DKUM: 11.03.2025; Views: 0; Downloads: 4 Full text (162,66 KB)This document has many files! More...
Abstract: Geodesic covering problems form a widely researched topic in graph theory. One such problem is geodetic problem introduced by Harary et al. Here we introduce a variation of the geodetic problem and call it strong edge geodetic problem. We illustrate how this problem is evolved from social transport networks. It is shown that the strong edge geodetic problem is NP-complete. We derive lower and upper bounds for the strong edge geodetic number and demonstrate that these bounds are sharp. We produce exact solutions for trees, block graphs, silicate networks and glued binary trees without randomization.Keywords: geodetic problem, strong edge geodetic problem, computational complexity, transport networksPublished in DKUM: 03.11.2017; Views: 1194; Downloads: 465 Full text (657,86 KB)This document has many files! More...
