International Journal of Mathematics Trends and Technology
Volume 66 | Issue 2 | Year 2020 | Article Id. IJMTT-V66I2P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I2P511
In this paper, we study the b-coloring of the product of paths and cycles. Let G be a graph with vertex set V(G) and edge E(G). The b-coloring is nothing but the b-chromatic number. The b-chromatic number is the largest integer k colors such that every color class has b-vertex. The b-vertex is the color dominating vertex that has an adjacent in all other color class. The b-chromatic number of a graph is denoted by φ(G).
[1] R.W. Irving, D.F. Manlove, The b-chromatic number of a graph, Discrete Appl. Math. 91(1999), 127-141.
[2] S.K. Vaidya and Rakhimol V.Issac, The b-chromatic number of some degree Splitting graphs, Malaya Journal of Mathematics, Vol. 2(3) (2014), 249-253.
[3] Kouider, M., Maheo, M., Some bounds for the b-chromatic number of a graph, Discrete Mathematics. 256,(2002),267-277.
[4] Kouider, M.,Zaker, M., Bounds for the b-chromatic number of some families of graphs, Discrete Math. 306,(2002),617-623.
[5] S.K. Vaidya and Rakhimol V.Issac, On the b-chromatic number of some graphs, Bulletin of the International Mathematical Virtual Institute, Vol. 5(2015), 191-195.
[6] T. R. Jensen and B. Toft, Graph colouring problems, John Wiley & Sons, 1995.
[7] M. Kubale, Graph colorings, American Mathematical Society, 2004.
[8] E. Kubicka and A. J. Schwenk, An introduction to chromatic sums, Proc. ACM Computer Science Conference, Louisville (Kentucky), 3945(1989).
[9] N. K. Sudev. S. Satheesh, K. P. Chithra and J. Kok, On certain colouring parameters of graphs, preprint.
A.Sulthana Afrose, S.Jamal Fathima, "b-Coloring of the Product of Paths and Cycles," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 2, pp. 105-109, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I2P511
PDF 
Abstract 
Keywords 
References 
Citation