%0 Journal Article %T Geodetic Number and Geo-Chromatic Number of 2-Cartesian Product of Some Graphs %A Medha Itagi Huilgol %A B. Divya %J Open Journal of Discrete Mathematics %P 1-16 %@ 2161-7643 %D 2022 %I Scientific Research Publishing %R 10.4236/ojdm.2022.121001 %X 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. %K Cartesian Product %K Grid Graphs %K Geodetic Set %K Geodetic Number %K Chromatic Set %K Chromatic Number %K Geo-Chromatic Set %K Geo-Chromatic Number %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=114598