b-Chromatic Number of M[C_n],M[P_n],M[F_1,n] and M[W_n]

Duraisamy Vijayalakshmi, Kandasamy Thilagavathi, Narayanan Roopesh

.

DOI: 10.4236/ojdm.2011.12010                

Abstract

In this paper, we discuss about the b-colouring and b-chromatic number for middle graph of Cycle, Path, Fan graph and Wheel graph denoted as M[C_n],M[P_n],M[F_1,n] and M[W_n] .

Keywords

Chromatic Number, b-Chromatic, b-Colouring, Middle Graph

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	S. Corteel, M. Valencia-Pabon, J.-C. Vera, “On Aproximating the b-chromatic Number,” Discrete Applied Mathematics, Vol. 146, No. 1, 2005, pp. 106-110. doi:10.1016/j.dam.2004.09.006
[2]	R. W. Irving and D. F. Manlove, “The b-chromatic Number of a Graph,” Discrete Applied Mathematics, Vol. 91, No. 1, 1999, pp. 127-141. doi:10.1016/S0166-218X(98)00146-2
[3]	M. Kouider, “b-chromatic Number of a Graph,” Subgraphs and Degrees Rappor interne LRI 1392.
[4]	V. J. Vernold, M. Venkatachalam and A. M. M. Akbar “A Note on Achromatic coloring of star graph families,” Filomat, Vol. 23, No. 3, 2009, pp. 251-255. doi:10.2298/FIL0903251V
[5]	K. Thilagavathi and N. Roopesh, “Generalization of Achromatic Colouring of Central Graphs”, Electronic Notes in Discrete Mathematics, Vol. 33, 2009, pp. 147-152. doi:10.1016/j.endm.2009.03.021
[6]	V. J. Vernold and A. M.M. Akbar, “On Harmonious Coloring of Middle Graph of C(Cn),C(K1,n) and C(Pn),” Note di Matematica, Vol. 29, No. 2, 2009, pp. 201-211.
[7]	H. Hajiabolhassan, “On the b-chromatic Number of Kneser Graphs,” Discrete Applied Mathematics, Vol. 158, No. 3, 2010, pp. 232-234. doi:10.1016/j.dam.2009.09.023
[8]	B. Effantin, “The b-chromatic Number of-power Graphs of Complete Caterpillars,” The Journal of Discrete Mathematical Sciences & Cryptography, Vol. 8, 2005, pp. 483-502.
[9]	C. T. Hoang and M. Kouider, “On the B-Dominating Colouring of Graphs,” Discrete Applied Mathematics, Vol. 152, No.1-3, 2005, pp. 176-186. doi:10.1016/j.dam.2005.04.001