| Issue |
RAIRO-Oper. Res.
Volume 52, Number 1, January–March 2018
|
|
|---|---|---|
| Page(s) | 205 - 216 | |
| DOI | https://doi.org/10.1051/ro/2018003 | |
| Published online | 30 May 2018 | |
Strong geodetic problem on Cartesian products of graphs
1
Institute of Mathematics, Physics and Mechanics,
Ljubljana, Slovenia
2
Faculty of Mathematics and Physics, University of Ljubljana,
Ljubljana, Slovenia
3
Faculty of Natural Sciences and Mathematics, University of Maribor,
Maribor, Slovenia
* Corresponding author: sandi.klavzar@fmf.uni-lj.si
Received:
5
August
2017
Accepted:
14
January
2018
The strong geodetic problem is a recent variation of the geodetic problem. For a graph G, its strong geodetic number sg(G) is the cardinality of a smallest vertex subset S, such that each vertex of G lies on a fixed shortest path between a pair of vertices from S. In this paper, the strong geodetic problem is studied on the Cartesian product of graphs. A general upper bound for sg(G □ H) is determined, as well as exact values for Km □ Kn, K1,k □ Pl, and prisms over Kn–e. Connections between the strong geodetic number of a graph and its subgraphs are also discussed.
Mathematics Subject Classification: 05C12 / 05C70 / 68Q17 / 68Q17
Key words: Geodetic problem / strong geodetic problem / isometric path problem / Cartesian product / subgraph
© EDP Sciences, ROADEF, SMAI 2018
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