Geodesic covering problems form a widely researched topic in graph theory. One such problem is geodetic problem introduced by Harary et al. [Math. Comput. Modelling, 1993, 17, 89-95]. 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.
@article{bwmeta1.element.doi-10_1515_math-2017-0101,
author = {Paul Manuel and Sandi Klav\v zar and Antony Xavier and Andrew Arokiaraj and Elizabeth Thomas},
title = {Strong edge geodetic problem in networks},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {1225-1235},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0101}
}
Paul Manuel; Sandi Klavžar; Antony Xavier; Andrew Arokiaraj; Elizabeth Thomas. Strong edge geodetic problem in networks. Open Mathematics, Tome 15 (2017) pp. 1225-1235. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0101/