Geodetic Number and Geo-Chromatic Number of 2-Cartesian Product of Some Graphs
Abstract: 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.
Cite this paper: Huilgol, M. and Divya, B. (2022) Geodetic Number and Geo-Chromatic Number of 2-Cartesian Product of Some Graphs. Open Journal of Discrete Mathematics, 12, 1-16. doi: 10.4236/ojdm.2022.121001.
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