A set
S ⊆ V (G) is called a geodetic set if every vertex of
G lies on a shortest
u-v path for some
u, v ∈ S, the minimum cardinality among all geodetic sets is called geodetic number and is denoted by
. A set
C ⊆ V (G) is called a chromatic set if
C contains all vertices of different colors in
G, the minimum cardinality among all chromatic sets is called the chromatic number and is denoted by
. A geo-chromatic set
Sc ⊆ V (G) is both a geodetic set and a chromatic set. The geo-chromatic number
of
G is the minimum cardinality among all geo-chromatic sets of
G. In this paper, we determine the geodetic number and the geo-chromatic number of 2-cartesian product of some standard graphs like complete graphs, cycles and paths.