TITLE:
Geodetic Number and Geo-Chromatic Number of 2-Cartesian Product of Some Graphs
AUTHORS:
Medha Itagi Huilgol, B. Divya
KEYWORDS:
Cartesian Product, Grid Graphs, Geodetic Set, Geodetic Number, Chromatic Set, Chromatic Number, Geo-Chromatic Set, Geo-Chromatic Number
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.12 No.1,
January
14,
2022
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.