THE b-CHROMATIC NUMBER OF HELM GRAPH

Main Article Content

Nadeem Ansari
R S Chandel
Rizwana Jamal

Abstract

The b-chromatic number ðœ‘(ðº) of a graph ðº is the greatest integer k such that ðº admits a proper k-coloring in which every color class ð‘– has a vertex realizing color ð‘– that is proficient to correspond with all the others color classes. The paper estimates the ð‘-chromatic number of helm graph, central graph of helm graph and middle graph of helm graph which is denoted by Hn, C(Hn) and ð‘€(Hn) respectively.

Downloads

Download data is not yet available.

Article Details

Section
Articles

References

Akbar Ali., M.M, Vivin, J.V., Harmonious chromatic

number of central graph of complete graph families,

Journal of Combinatorics, Information and System

Sciences, no. 1- 4 (combined) 32, 2007, 221–231.

Balakrishnan, R., Raj, S.F., Bounds for the b-chromatic

number of the Mycielskian of some families of graphs.

Ars Combinatoria, 122, 2015, pp. 89-96.

Chaouche, F., Berrachedi, A., Some bounds for the bchromatic

number of a generalized Hamming graphs, Far

East J. Appl. Math. 26, 2007, 375–391.

Corteel, S., Valencia-Pabon, M., Vera, J.C., On

approximating the b-chromatic number. Discrete Applied

Mathematics, 146(1), 2005, 106-110.

Harary, F., Graph Theory, Narosa Publishing home, 2001.

Hoang, C.T., Kouider, M., On the b-dominating coloring

of graphs, Discrete Applied Maths, 152 no.1-3, 2005,

-186.

Kouider, M., Maheo, M., Some bounds for the bchromatic

number of a graph, Discrete Math. 256, 2002,

-277.

Kouider, M., b-chromatic number, subgraphs and degrees,

Technical Report N1392, LRI, Universite de Paris Swd,

Kouider, M., Zaker, M., Bounds for the b-chromatic

number of some families of graphs. Discrete Math. 306,

, 617-623.

Kouider, M., Maheo, M, The b-Chromatic number of

Cartesian product of two graphs, Studia Sci. Math.

Hungar. 44, 2007, 49-55.

Kratochvil, J., Tuza, Z., Voigt, M., On the b-chromatic

number of graphs. In International Workshop on Graph-

Theoretic Concepts in Computer Science, Springer Berlin

Heidelberg, 2002, pp. 310-320.

R. Irving and D. Manlove, The b-chromatic number of a

graph. Discrete Appl. Math. 91, 1999, 127-141.

Vijayalaksmi, D., Thialagavathi, K, Roopesh, N., A note

on b-chromatic number of star graph families Bulletin of

Pure and Applied Sciences Volume 30 Issue No. 1, 2011,

-24.

Vivin, J.V., Venkatachalam, M., The b-chromatic number

of corona graphs, Utilitas Mathematicae 88, 2012, 299-

Vivin, J.V., Vekatachalam, M., On b-chromatic number

of sun let graph and wheel graph families. Journal of the

Egyptian Mathematical Society, 23(2), 2015, pp. 215-218.