CHROMATIC WEAK DOMATIC PARTITION IN GRAPHS

Year 2019, Volume: 9 Issue: 2, 279 - 286, 01.06.2019

P. Aristotle S. Balamurugan P. P. Lakshmi V. Swaminathan

Abstract

In a simple graph G, a subset D of V G is called a chromatic weak dom- inating set if D is a weak dominating set and  < D > =  G . Similar to domatic partition, chromatic weak domatic partition can be dened. The maximum cardinality of a chromatic weak domatic partition is called the chromatic weak domatic number of G. Bounds for this number are obtained and new results are derived involving chromatic weak domatic number and chromatic weak domination number.

Keywords

Domatic number, Weak domatic number, Chromatic weak domatic number.

References

• [1] Balamurugan, S., (2008), A study of Chromatic strong domination in graphs, Ph.D Thesis, Madurai Kamaraj University, India.
• [2] Cockayne, E. J., and Hedetniemi, S. T., (1977), Towards a theory of domination in graphs, Networks, pp. 247 - 261.
• [3] Harary, F., (1972), Graph Theory, Addison Wesley, reading Mass.
• [4] Hattingh, J. H., and Laskar, R. C., (1998), On weak domination in graphs, Ars Combinatoria 49, pp. 205 - 216.
• [5] Haynes, T. W., Hedetniemi, S. T., and Slater, P. J., (1998), Fundamentals of Domination in Graphs, Marcel Dekker Inc.. New york.
• [6] Haynes, T. W., Hedetniemi, S. T., and Slater, P. J., (1998), Domination in Graphs: Advanced Topics, Marcel Dekker, Inc..
• [7] Janakiraman, T. N., Poobalaranjani, M., (2010), On the Chromatic Preserving Sets, International Journal of Engineering Science, Advanced Computing and Bio-Technology, Vol. 1, No. 1, pp. 29 - 42.
• [8] Janakiraman, T. N., Poobalaranjani, M., (2010), Dom-Chromatic Sets in Bipartite Graphs, International Journal of Engineering Science, Advanced Computing and Bio-Technology, Vol. 1, No. 2, pp. 80 - 95.
• [9] Janakiraman, T. N., Poobalaranjani, M., (2011), Dom-Chromatic Sets of Graphs, International Journal of Engineering Science, Advanced Computing and Bio-Technology, Vol. 1, No. 2, pp. 88 - 103.
• [10] Poobalaranjani, M., (2006), On Some Coloring and Domination Parameters in Graphs, Ph.D Thesis, Bharathidasan University, India.
• [11] Rautenbach, D., (1998), Bounds on the weak domination number, Austral. J. Combin. 18, pp. 245 - 251.
• [12] Sampathkumar, E., Pushpa Latha, L., (1996), Strong weak domination and domination balance in a graph, Discrete Mathematics, 161, pp. 235 - 242.
• [13] Selvalakshmi, P., Balamurugan, S., Aristotle, P., and Swaminathan, V., A note on Chromatic weak dominating sets in Graphs, Submitted