International Journal of Mathematics Trends and Technology
Volume 54 | Number 3 | Year 2018 | Article Id. IJMTT-V54P528 | DOI : https://doi.org/10.14445/22315373/IJMTT-V54P528
Equations
connecting two parameters of a graph have already been studied. For example,๐ธ ๐ฎ + ๐ ๐ฎ = ๐ or ๐ โ ๐ or ๐ ๐ฎ + ๐ ๐ฎ = ๐or ๐ โ ๐. A subset S of G is called a
neighbourhood chromatic dominating set if S is a dominating set and ๐ < ๐ ๐บ > = ๐(๐ฎ) . The minimum cardinality of a
neighbourhood chromatic dominating set of ๐ฎ is called the neighbourhood chromatic domination
number of G and is denoted by ๐ธ๐๐๐๐
(๐ฎ). In this paper, graph equation ๐ธ๐๐๐๐
๐ฎ + ๐ ๐ฎ = ๐ is solved for ๐ ๐ฎ = ๐ or ๐ or ๐ or ๐ โ ๐. Further ๐ธ๐๐๐๐
๐ฎ + ๐ ๐ฎ = ๐ โ ๐ is solved for ๐ ๐ฎ = ๐ โ ๐.
[1] S. Balamurgan, P. Aristotle, V. Swaminathan and G. Prabakaran, On Graphs whose Neighbourhood Chromatic Domination Number is two, Proceedings of the National Conference on Recent Developments on Emerging Fields in Pure and Applied Mathematics, ISBN No. 978-93-83209-02-6, Vol. 1, pp. 88 โ 99, India 2015.
[2] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker Inc.. New York, 1998.
[3] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Domination in Graphs: Advanced Topics, Marcel Dekker, Inc.. 1998.
P. Aristotle, S. Balamurugan, V. Swaminathan, "Graphical Equations on Neighbourhood Chromatic Domination," International Journal of Mathematics Trends and Technology (IJMTT), vol. 54, no. 3, pp. 253-261, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V54P528
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