# Strong edge geodetic problem in networks

Paul Manuel; Sandi Klavžar; Antony Xavier; Andrew Arokiaraj; Elizabeth Thomas

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 1225-1235
- ISSN: 2391-5455

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topPaul 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 -

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