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.
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![\"\"](\"Edit_82259359-0135-4a65-9378-b767f0405b48.png\")
. 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 ![\"\"](\"Edit_d849148d-5778-459b-abbb-ff25b5cd659b.png\")
. A geo-chromatic set Sc ？ V (G) is both a geodetic set and a chromatic set. The geo-chromatic number ![\"\"](\"Edit_505e203c-888c-471c-852d-4b9c2dd1a31c.png\")
？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.
