Volume 66 | Issue 1 | Year 2020 | Article Id. IJMTT-V66I1P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I1P507
In this paper we found minimum cardinality among all geodetic sets which is known as geodetic number and is denoted by g(G) and the minimum cardinality among all the chromatic sets which is known as chromatic number and is denoted by x(G) . The combination of these concepts we have the geo chromatic number xgc(G) for certain cartesian product of graphs.
[1] J.A. Bondy and U.S.R. Murthy, ―Graph Theory with Applications‖, Macmillon London and Elsevier New York, 1976.
[2] F. Buckley and F. Harary, ―Distance in Graphs‖, Addison – Wesly Publishing company, Redwood city, CA, 1990.
[3] Beulah Samli. S, Robinson Chellathurai__Geo Chromatic Number of a Graph – Published on ISROSET Volume-5, Issue-6, pp.259-264, December (2018)
[4] H. Escuardo, R. Gera, A. Hansberg, N. Jafari Rad and L. Volkmann,―Geodetic Domination in graphs‖, J. Combin. Math Combin. Comput. 77 (2011), 89-101.
[5] Gary Chatrand and P.Zhang, ―Introduction to Graph Theory‖, MacGraw Hill, 2005.
[6] Gary Chatrand, F. Harary and P. Zhang, ―On the geodetic number of a graph‖, Networks, 39 (2002), 1-6.
[7] Gary Chatrand, F. Harary and P. Zhang, ―Geodetic sets in graphs‖, DiscussionesMathematicae Graph Theory
[8] A. Haneberg and L. Volkmann, ―On the geodetic and geodetic domination numbers of a graph‖, Discrete Mathematics 310 (2010), 2140 – 2146.
[9] M. Mohammed Abdul Khayoom and P. Arul Paul Sudhahar,―Monophonic Chromatic Parameter in a Connected Graph‖, International Journal of Mathematical Analysis 11 (2017), no.19,
Dr.Sr.A. Stanis Arul Mary, "Geo Chromatic Number for certain Cartesian product of Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 1, pp. 40-43, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I1P507