Strong edge geodetic problem in networks

Paul Manuel, et al. "Strong edge geodetic problem in networks." Open Mathematics 15.1 (2017): 1225-1235. <http://eudml.org/doc/288308>.

@article{PaulManuel2017,
abstract = {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.},
author = {Paul Manuel, Sandi Klavžar, Antony Xavier, Andrew Arokiaraj, Elizabeth Thomas},
journal = {Open Mathematics},
keywords = {Geodetic problem; Strong edge geodetic problem; Computational complexity; Transport networks},
language = {eng},
number = {1},
pages = {1225-1235},
title = {Strong edge geodetic problem in networks},
url = {http://eudml.org/doc/288308},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Paul Manuel
AU - Sandi Klavžar
AU - Antony Xavier
AU - Andrew Arokiaraj
AU - Elizabeth Thomas
TI - Strong edge geodetic problem in networks
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 1225
EP - 1235
AB - 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.
LA - eng
KW - Geodetic problem; Strong edge geodetic problem; Computational complexity; Transport networks
UR - http://eudml.org/doc/288308
ER -