A Study on Double Geo Chromatic Number of Line Graph of Some Graph Families

R. Joseph Paul¹ , S. Beulah Samli² , U. Mary³

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.2 , pp.7-11, Apr-2022

Online published on Apr 30, 2022

Copyright © R. Joseph Paul, S. Beulah Samli, U. Mary . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

Abstract :
The double geo chromatic number of G is the minimum cardinality of a double geo chromatic set of G. If any u ? v geodesic, where u, v ? S includes at least two entire color classes of G, it is said to be a double geo chromatic set Sdg. This concept has been used to estimate the double geo chromatic numbers of line graphs and to derive certain general features and also some of the existing research has also been found to be inaccurate.

Key-Words / Index Term :
Geodetic Number, Chromatic Number, Geo Chromatic Number, Double Geo Chromatic Number

References :
[1] .A. Ahangar, “Graph with large geodetic number,” Filomat, Vol.31, Issue 13, pp.4297-4304, 2017
[2] S.B. Samli, S.R. Chellathurai, “Geo chromatic number of a graph,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue 6, pp.259-264, 2018.
[3] F. Buckley, F. Harary, “Distance in Graphs,” Addison - Wesly Publishing company, Redwood City, CA, 1990.
[4] G. Chatrand, P. Zhang, “Introduction to Graph Theory,” MacGraw Hill, 2005.
[5] G. Chatrand, F. Harary, P. Zhang, “On the geodetic number of a graph,” Networks, Vol.39, Issue 1, pp.1-6, 2002.
[6] G. Chatrand, F. Harary, P. Zhang, “Geodetic sets in graphs,” Discuss. Math., Graph Theory, Vol.20, Issue 1, pp.129-138, 2000.
[7] H. Escuardo, R. Gera, A. Hansberg, N. Jafari Rad, L. Volkmann, “Geodetic domination in graphs,” J. Comb. Math. Comb. Comput, Vol 77, pp.89-101, 2011.
[8] A. Hansberg, L. Volkmann, “On the geodetic and geodetic domination numbers of a graph,” Discrete Math., Vol 310, Issue 15, pp.2140-2146, 2010.
[9] F. Harary. “Graph Theory,” Addison - Wesley, 1969.
[10] F. Harary, E. Loukakis, C. Tsouros, “The geodetic number of a graph,” Math. Comput. Modelling , Vol 17, Issue 11, pp.89-95, 1993.
[11] M. Mohammed Abdul Khayoom, P. Arul Paul Sudhahar, “Monophonic chromatic parameter in a connected graph,” Int. J. Math. Anal., Ruse, Vol.11, Issue 19, pp.911-920, 2017.
[12] A.P. Santhakumaran, J. John, “Edge geodetic number of a graph”, J. Discrete Math. Sci. and Cryptograpy, Vol.10, Issue 3, pp.415-432, 2007.
[13] A.P. Santhakumaran, T. Jebaraj, “Double geodetic mumber of a graph,” Discuss. Math. Graph Theory, Vol. 32, Issue 1, pp. 109-119, 2012.
[14] S. Beulah Samli, J. John, S. Robinson Chellathurai, “The Double Geo Chromatic Number of a graph,” Bulletin of the international Mathematical Virtual Institute, Vol.11, Issue 1, pp.25-38, 2021.
[15] V.M. Goudar, K. S. Ashalatha, Venkatesh, M.H. Muddebihal , “On the Geodetic number of Line Graph,” Int. J. Contemp. Math. Sci, Vol. 7, Issue 46, pp.2289-2295, 2012.