A set S_c⊆V(G) is said to be a geo chromatic set of G if S_c is both a geodetic set and a chromatic set of G . The minimum cardinality among all geo chromatic sets of a graph G is the geo chromatic number and is denoted by χ_gc (G) . A set of extreme vertices E of G is said to be a weak extreme chromatic set if Ext(G) is a chromatic set of G. A weak extreme chromatic set is denoted by WExt(G) and the number of extreme vertices in WExt(G) is its weak extreme order χ_w (G). A graph G is an extreme geo chromatic graph if χ_gc (G) = ex(G). Bounds for the geo chromatic number of strong product graphs are obtained.