Strong geodetic problem on Cartesian products of graphs
RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 1, pp. 205-216.

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 K m □ K n , K 1 , k □ P l , and prisms over □ K, and prisms over K n - e . Connections between the strong geodetic number of a graph and its subgraphs are also discussed.–e. Connections between the strong geodetic number of a graph and its subgraphs are also discussed.

DOI : 10.1051/ro/2018003
Classification : 05C12, 05C70, 68Q17, 68Q17
Mots-clés : Geodetic problem, strong geodetic problem, isometric path problem, Cartesian product, subgraph
Iršič, Vesna 1 ; Klavžar, Sandi 1

1 
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Iršič, Vesna; Klavžar, Sandi. Strong geodetic problem on Cartesian products of graphs. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 1, pp. 205-216. doi : 10.1051/ro/2018003. http://www.numdam.org/articles/10.1051/ro/2018003/

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