Volume 52, Number 1, January–March 2018
|Page(s)||205 - 216|
|Published online||30 May 2018|
Strong geodetic problem on Cartesian products of graphs
Institute of Mathematics, Physics and Mechanics,
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: email@example.com
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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