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 certain prisms.
Connections between the strong geodetic number of a graph and its subgraphs are
also discussed.Comment: 18 pages, 9 figure