The geodetic number of strong product graphs

For two vertices u and v of a connected graph G, the set ${\displaystyle I_G[u,v]}$ consists of all those vertices lying on u-v geodesics in G. Given a set S of vertices of G, the union of all sets ${\displaystyle I_G[u,v]}$ for u,v ∈ S is denoted by ${\displaystyle I_G\left[S\right]}$. A set S ⊆ V(G) is a geodetic set if ${\displaystyle I_G\left[S\right]=V\left(G\right)}$ and the minimum cardinality of a geodetic set is its geodetic number g(G) of G. Bounds for the geodetic number of strong product graphs are obtainted and for several classes improved bounds and exact values are obtained.